Main Analysis CATegories

Load packages

library(tidyverse)
library(janitor)
library(cowplot)
library(here)
library(readxl)
library(Matrix)
library(lme4)
library(lmerTest)
library(TOSTER)
library(wesanderson)
library(gghalves)
library(car)
library(multilevelTools)
library(JWileymisc)
library(broom.mixed)
library(papaja)
library(effectsize)
library(ggimage)
library(sessioninfo)
library(broom)
source("compute_iccs.R")
source("common.R")

theme_set(theme_cowplot())

knitr::opts_chunk$set(cache = FALSE, warn = FALSE,warning=FALSE, message = FALSE)

Load data

#set paths
data_file_path <- here::here("..","..","data","processed_data","CATegories_exp2_processed_data_with_exclusion_info.csv")
useable_trial_summary_path <- here::here("..","..","data","processed_data","CATegories_exp2_useable_trial_summary.csv")
summarize_subj_trials_path <- here::here("..","..","data","processed_data","CATegories_exp2_trial_summary_data.csv")
participant_data_path <- here::here("..","..","data","processed_data","CATegories_exp2_processed_participant_data_anonymized.csv")
resampled_data_file_path <- here::here("..","..","data","processed_data","CATegories_exp2_processed_data_resampled.csv")
#load data
d <- read_csv(data_file_path) 
participant_total_useable_trials <- read_csv(useable_trial_summary_path)
summarize_subj_trials <- read_csv(summarize_subj_trials_path)
participant_data <- read_csv(participant_data_path)
d_resampled <- read_csv(resampled_data_file_path) #note that this file gets created in cluster_permutation_analysis.Rmd

Useable trial summary

In order for a trial to be included, participants must contribute at least 50% looking during the windows of interest when computing baseline-corrected proportion target looking: the critical window (300 ms - 2800 ms relative to target word onset) and the baseline window (-2000 ms - 0 ms relative to target word onset). See 2_process_exclusions.Rmd for detailed processing steps.

Overall, among the trials contributed by 141 participants (excluding 2 participants whose data was filtered out earlier in the process, because they either did not provide any useable trials or due to parent interference throughout the session), 80.9% of trials contained sufficient looking to meet our trial-level inclusion criteria (at least 50% looking during both the baseline window and the critical window). Overall, after additional trial-level exclusions (due technical errors or frame rate issues), 78.3% were retained. 84 of the 141 participants contributed valid data on at least half of the experimental trials (for all participants: M = 25.9; only for included participants: M = 36.8).

Summarize participant information

All participants contributing data

participant_data_summarized <- participant_data %>%
  summarize(
    N=length(unique(sub_num)),
    num_sessions = sum(session<3),
    session_1_N = sum(session==1),
    session_2_N = sum(session==2)
  )

participant_data_summarized %>%
  knitr::kable()

N	num_sessions	session_1_N	session_2_N
143	255	143	112

participant_data_summarized <- participant_data %>%
  distinct(sub_num,session_1_data,session_2_data) %>%
  left_join(participant_total_useable_trials)

#participants without session 2 data who were subsequently excluded
sum(filter(participant_data_summarized,session_2_data=="N")$exclude_participant)

## [1] 27

#participants with session 2 data who were subsequently excluded
sum(filter(participant_data_summarized,session_2_data=="Y")$exclude_participant)

## [1] 32

All participants providing coded looking data

#summarize subj info
subj_info_multisession <- d %>%
  distinct(sub_num, age,age_mo,child_gender,trial_order) %>%
  mutate(
    age_mo_c = age_mo - mean(age_mo),
    age_c = age - mean(age)
  )

subj_info <- d %>%
  distinct(sub_num,child_gender) %>%
  summarize(
    N = n(),
    N_female = sum(child_gender=="f")
  )

overall_subj_info <- subj_info_multisession %>%
  summarize(
    N = length(unique(sub_num)),
    sessions = n(),
    mean_age = mean(age_mo),
    min_age = min(age),
    max_age = max(age),
    sd_age = sd(age_mo)
  ) %>%
  left_join(subj_info)
  
overall_subj_info %>%
  knitr::kable()

N	sessions	mean_age	min_age	max_age	sd_age	N_female
141	248	15.73065	410	718	1.613515	70

All included participants

# subjects with usable trial data only
subj_info_multisession_usable_trials <- d %>%
  filter(exclude_participant==0) %>%
  distinct(sub_num, age,age_mo,child_gender,trial_order) %>%
  mutate(
    age_mo_c = age_mo - mean(age_mo),
    age_c = age - mean(age)
  )

subj_info_usable_trials <- d %>%
  filter(exclude_participant==0) %>%
  filter(useable_window==1) %>%
  distinct(sub_num,child_gender) %>%
  summarize(
    N = n(),
    N_female = sum(child_gender=="f")
  )

overall_subj_info_usable_trials <- subj_info_multisession_usable_trials %>%
  summarize(
    N = length(unique(sub_num)),
    sessions = n(),
    mean_age = mean(age_mo),
    mean_age_days=mean(age),
    min_age = min(age),
    max_age = max(age),
    sd_age = sd(age_mo)
  ) %>%
  left_join(subj_info_usable_trials)
  
overall_subj_info_usable_trials %>%
  knitr::kable()

N	sessions	mean_age	mean_age_days	min_age	max_age	sd_age	N_female
84	164	15.70122	477.8963	410	574	1.490131	51

Demographics of final useable sample

Next, we summarize demographic information for the final sample (removing participant exclusions).

demographics_summary <- d %>%
  filter(exclude_participant == 0) %>%
  distinct(sub_num,demographic_us_race_ethnicity_identification,demographic_education_level,demographic_annual_income,demographic_country,demographic_state,demographic_density)

Race/ Ethnicity

multiple_categories_list <- c("White, Middle Eastern or North African","White, Hispanic, Latino, or Spanish origin","White, Black or African American, Middle Eastern or North African","White, Black or African American","White, Asian, Middle Eastern or North African","White, Asian","Hispanic, Latino, or Spanish origin, Black or African American","Hispanic, Latino, or Spanish origin, Asian","Black or African American, Asian","Asian, Middle Eastern or North African")

race_ethnicity <- demographics_summary %>%
  group_by(demographic_us_race_ethnicity_identification)%>%
  summarize(
    N = n()
  ) %>%
  ungroup() %>%
  mutate(percent=N/sum(N),
         multiple_categories=ifelse(demographic_us_race_ethnicity_identification %in% multiple_categories_list,1,0))
#percent reporting multiple categories
sum(filter(race_ethnicity,multiple_categories==1)$N)/sum(race_ethnicity$N)

## [1] 0.2261905

#quick visualization
ggplot(demographics_summary,aes(y=demographic_us_race_ethnicity_identification)) +
  geom_bar()

Parent Income

income <- demographics_summary %>%
  group_by(demographic_annual_income)%>%
  summarize(
    N = n()
  )

income %>%
  knitr::kable()

demographic_annual_income	N
100000	6
110000	1
120000	5
130000	4
140000	1
15000	1
150000	11
160000	1
170000	1
180000	1
190000	1
20000	1
30000	1
40000	4
50000	7
60000	5
70000	4
80000	5
90000	3
>200000	19
NA	2

#quick visualiztion
ggplot(demographics_summary,aes(demographic_annual_income)) +
  geom_bar()+
  theme(axis.text.x = element_text(angle = 90))

Parent Education Level

education <- demographics_summary %>%
  group_by(demographic_education_level)%>%
  summarize(
    N = n()
  )

education %>%
  knitr::kable()

demographic_education_level	N
assoc	1
bach	31
col	2
grad	3
hs	1
prof	46

Geographic Information

states <- demographics_summary %>%
  group_by(demographic_state)%>%
  summarize(
    N = n()
  )

ggplot(demographics_summary,aes(demographic_state)) +
  geom_bar()+
  theme(axis.text.x = element_text(angle = 90))

population_density <- demographics_summary %>%
  group_by(demographic_density) %>%
  summarize(
    N = n()
  )
population_density %>%
  knitr::kable()

demographic_density	N
rural	4
suburban	57
urban	22
NA	1

Summarize Overall Target Looking by Participant

Here, we summarize each participants’ average accuracy during the critical window and average baseline-corrected proportion target looking.

# save key columns
key_cols_summarized_trial_data <- c(
  "sub_num","session", "age","age_mo","days_between_sessions", "child_gender", "trial_order","trial_number","condition","target_image","distractor_image","target_category","distractor_category","target_typicality_z","distractor_typicality_z","target_parent_typicality_rating","distractor_parent_typicality_rating","target_parent_typicality_rating_z","distractor_parent_typicality_rating_z","target_parent_typicality_by_category_z","distractor_parent_typicality_by_category_z","mean_target_looking_critical","mean_target_looking_baseline","corrected_target_looking","exclude_participant","age_exclusion","trial_exclusion","trial_exclusion_reason","exclude_technical_issue","exclude_frame_rate","useable_window","useable_critical_window","useable_baseline_window","useable_window_short","total_trials_short","exclude_participant_insufficient_data_short","mean_target_looking_critical_short","corrected_target_looking_short")

#extract summarized trial-level accuracy (see 2_process_exclusions.Rmd for details on how summarized columns are computed)
trial_corrected_accuracy_all <- d %>%
  select(all_of(key_cols_summarized_trial_data)) %>%
  distinct()

trial_corrected_accuracy <- trial_corrected_accuracy_all %>%
  filter(exclude_participant==0) %>%
  filter(trial_exclusion==0)

# summarize average accuracy
avg_corrected_target_looking <- trial_corrected_accuracy  %>%
  group_by(sub_num) %>%
  summarize(N=n(),
            mean_age = mean(age),
            mean_age_mo = mean(age_mo),
            average_corrected_target_looking=mean(corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=average_corrected_target_looking-ci,
            upper_ci=average_corrected_target_looking+ci,
            average_critical_window_looking=mean(mean_target_looking_critical,na.rm=TRUE),
            critical_window_ci = qt(0.975, N-1)*sd(mean_target_looking_critical,na.rm=T)/sqrt(N),
            critical_window_lower_ci=average_critical_window_looking-critical_window_ci,
            critical_window_upper_ci=average_critical_window_looking+critical_window_ci)

#baseline-corrected target looking summarized overall
overall_corrected_target_looking <- avg_corrected_target_looking %>%
  summarize(N=n(),
            corrected_target_looking=mean(average_corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(average_corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=corrected_target_looking-ci,
            upper_ci=corrected_target_looking+ci)
overall_corrected_target_looking %>%
  knitr::kable()

N	corrected_target_looking	ci	lower_ci	upper_ci
84	0.0711788	0.0168447	0.0543341	0.0880235

By Typicality Condition

We summarize each participants’ average accuracy during the critical window and average baseline-corrected proportion target looking, split by typicality condition.

# summarize average accuracy within participant
avg_corrected_target_looking_by_typicality <- trial_corrected_accuracy  %>%
  group_by(sub_num, condition) %>%
  summarize(N=n(),
            mean_age = mean(age),
            mean_age_mo = mean(age_mo),
            average_corrected_target_looking=mean(corrected_target_looking,na.rm=TRUE),
            se=sd(corrected_target_looking,na.rm=T)/sqrt(N),
            ci=qt(0.975, N-1)*sd(corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=average_corrected_target_looking-ci,
            upper_ci=average_corrected_target_looking+ci,
            lower_se=average_corrected_target_looking-se,
            upper_se=average_corrected_target_looking+se,
            average_critical_window_looking=mean(mean_target_looking_critical,na.rm=TRUE),
            critical_window_ci = qt(0.975, N-1)*sd(mean_target_looking_critical,na.rm=T)/sqrt(N),
            critical_window_lower_ci=average_critical_window_looking-critical_window_ci,
            critical_window_upper_ci=average_critical_window_looking+critical_window_ci)

#baseline-corrected target looking summarized overall
overall_corrected_target_looking_by_typicality <- avg_corrected_target_looking_by_typicality %>%
  group_by(condition) %>%
  summarize(N=n(),
            corrected_target_looking=mean(average_corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(average_corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=corrected_target_looking-ci,
            upper_ci=corrected_target_looking+ci)

overall_corrected_target_looking_by_typicality %>%
  knitr::kable()

condition	N	corrected_target_looking	ci	lower_ci	upper_ci
atypical	84	0.0647849	0.0193507	0.0454342	0.0841356
typical	84	0.0795095	0.0218702	0.0576393	0.1013797

By Target Label

We summarize each participants’ average accuracy during the critical window and average baseline-corrected proportion target looking, split by typicality condition and target label.

# summarize average accuracy within participant
avg_corrected_target_looking_by_category <- trial_corrected_accuracy  %>%
  group_by(sub_num, condition,target_category) %>%
  summarize(N=n(),
            mean_age = mean(age),
            mean_age_mo = mean(age_mo),
            average_corrected_target_looking=mean(corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=average_corrected_target_looking-ci,
            upper_ci=average_corrected_target_looking+ci,
            average_critical_window_looking=mean(mean_target_looking_critical,na.rm=TRUE),
            critical_window_ci = qt(0.975, N-1)*sd(mean_target_looking_critical,na.rm=T)/sqrt(N),
            critical_window_lower_ci=average_critical_window_looking-critical_window_ci,
            critical_window_upper_ci=average_critical_window_looking+critical_window_ci)

Main Analyses

Aim 1

1.1

1.1.1.

To investigate whether there was an effect of typicality on infants’ word recognition,we fit a linear mixed-effects model predicting average baseline-corrected proportion target looking from typicality condition (centered), including a by-participant random intercept. No random slope was included because the number of observations in the model would otherwise be equal to the number of random effects - however, a model with (overriding the lmer error message) or without typicality condition as a random slope yields identical results.

avg_corrected_target_looking_by_typicality <- avg_corrected_target_looking_by_typicality %>%
  mutate(
    typicality_condition_c = case_when(
      condition == "atypical" ~ -0.5,
      condition == "typical" ~ 0.5,
      TRUE ~ NA_real_
    ),
    typicality_condition_typ = case_when(
      condition == "atypical" ~ -1,
      condition == "typical" ~ 0,
      TRUE ~ NA_real_
    ),
    typicality_condition_atyp = case_when(
      condition == "atypical" ~ 0,
      condition == "typical" ~ 1,
      TRUE ~ NA_real_
    ),
  )

m_1_1 <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_c + (1+typicality_condition_c|sub_num),data=avg_corrected_target_looking_by_typicality,control=lmerControl(check.nobs.vs.nlev= "ignore",check.nobs.vs.nRE= "ignore"))

#Note that we ignore the warning here that number of observations is equal to the number of random effects, which lmer dislikes due to making it impossible to separate error at different hierarchical levels
#however, the model fit (at the fixed level) is for all intents and purposes identical for the model retaining the random slope for typicality and one removing the random slope for typicality
#(see commented-out model below)
#we therefore proceed with the (numerically identical) model with the random slope retained, for consistency with the Stage 1 plan.
#This same rationale applies to subsequent participant-level models we fit below.

#m_1_1 <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_c + (1|sub_num),data=avg_corrected_target_looking_by_typicality)

summary(m_1_1)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_corrected_target_looking ~ 1 + typicality_condition_c +  
##     (1 + typicality_condition_c | sub_num)
##    Data: avg_corrected_target_looking_by_typicality
## Control: 
## lmerControl(check.nobs.vs.nlev = "ignore", check.nobs.vs.nRE = "ignore")
## 
## REML criterion at convergence: -310.8
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.13730 -0.38265  0.05135  0.39401  1.82405 
## 
## Random effects:
##  Groups   Name                   Variance Std.Dev. Corr
##  sub_num  (Intercept)            0.003995 0.06320      
##           typicality_condition_c 0.004733 0.06880  0.25
##  Residual                        0.003876 0.06225      
## Number of obs: 168, groups:  sub_num, 84
## 
## Fixed effects:
##                         Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)             0.072147   0.008404 83.000327   8.585 4.42e-13 ***
## typicality_condition_c  0.014725   0.012191 82.999799   1.208    0.231    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.128 
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model is nearly unidentifiable: large eigenvalue ratio
##  - Rescale variables?

confint(m_1_1,method="Wald")

##                               2.5 %     97.5 %
## .sig01                           NA         NA
## .sig02                           NA         NA
## .sig03                           NA         NA
## .sigma                           NA         NA
## (Intercept)             0.055675942 0.08861852
## typicality_condition_c -0.009169538 0.03861872

Infants successfully recognized the target words (Model Intercept: b=0.07, 95% CI [0.06, 0.09], t(83) = 8.59, p< .001).

Overall Typicality Effect Plot

Next, we plot the overall average base-line corrected proportion target looking for each condition (in black). Individual points represent individual subjects, lines link subject responses between conditions. Error bars represent 95% CIs.

#Overall baseline-corrected proportion target looking by condition
pal <- wes_palette("Rushmore1", n=5)
set.seed(1)
jitterer <- position_jitter(width = .05,seed=1)
p0 <- ggplot(avg_corrected_target_looking_by_typicality,aes(x=condition,y=average_corrected_target_looking, fill=condition))+
  geom_half_violin(data=filter(avg_corrected_target_looking_by_typicality, condition=="atypical"),position = position_nudge(x = -.1, y = 0), width=1,trim = FALSE, alpha = .8,color=NA,side="l")+
  geom_half_violin(data=filter(avg_corrected_target_looking_by_typicality, condition=="typical"),position = position_nudge(x = .1, y = 0), width=1,trim = FALSE, alpha = .8,color=NA,side="r")+
  geom_path(aes(group=sub_num),color="black",fill=NA,alpha=0.15,size=0.75,position=jitterer)+
  geom_point(aes(color=condition,group=sub_num), size = 2.5, alpha=0.15,position=jitterer)+
  geom_point(data=overall_corrected_target_looking_by_typicality,aes(y=corrected_target_looking),color="black",size=5)+
  geom_line(data=overall_corrected_target_looking_by_typicality,aes(y=corrected_target_looking,group=1),color="black",size=3)+
  geom_errorbar(data=overall_corrected_target_looking_by_typicality,aes(y=corrected_target_looking,ymin=lower_ci,ymax=upper_ci),width=0,size=1.2,color="black")+
  #geom_boxplot(outlier.shape = NA, alpha = .5, width = .1, colour = "black")+
  #scale_colour_brewer(palette = "Dark2")+
  #scale_fill_brewer(palette = "Dark2")+
  geom_hline(yintercept=0,linetype="dashed")+
  scale_colour_manual(values=pal[c(3,4)])+
  scale_fill_manual(values=pal[c(3,4)])+
  theme(legend.position="none")+
  xlab("Typicality Condition")+
  ylab("Baseline-Corrected\nProportion Target Looking")+
  theme(axis.title.x = element_text(face="bold", size=20),
        axis.text.x  = element_text(size=14),
        axis.title.y = element_text(face="bold", size=20),
        axis.text.y  = element_text(size=16),
        strip.text.x = element_text(size = 16,face="bold"))

p0

ggsave(here::here("..","figures","baseline_corrected_accuracy_overall.png"),width=7,height=6)

1.1.2

overall_condition_summary <- avg_corrected_target_looking_by_typicality %>%
  ungroup() %>%
  group_by(sub_num) %>%
  summarize(
    condition_diff = average_corrected_target_looking[condition=="typical"]-average_corrected_target_looking[condition=="atypical"]
  ) %>%
  ungroup() %>%
  summarize(
    N=n(),
    diff = mean(condition_diff),
    sd = sd(condition_diff)
  )

tsum_TOST(m1=overall_condition_summary$diff,sd1=overall_condition_summary$sd,n1=overall_condition_summary$N,eqb=0.25, eqbound_type = "SMD")

## 
## One-sample t-Test
## 
## The equivalence test was non-significant, t(83) = -1.083, p = 1.41e-01
## The null hypothesis test was non-significant, t(83) = 1.208, p = 2.31e-01
## NHST: don't reject null significance hypothesis that the effect is equal to zero 
## TOST: don't reject null equivalence hypothesis
## 
## TOST Results 
##                 t df p.value
## t-test      1.208 83   0.231
## TOST Lower  3.499 83 < 0.001
## TOST Upper -1.083 83   0.141
## 
## Effect Sizes 
##            Estimate      SE              C.I. Conf. Level
## Raw         0.01472 0.01219  [-0.0056, 0.035]         0.9
## Hedges's g  0.13059 0.10957 [-0.0484, 0.3088]         0.9
## Note: SMD confidence intervals are an approximation. See vignette("SMD_calcs").

There was no significant effect of typicality, b=0.01, 95% CI [-0.009, 0.04], t(83)=1.20, p=.23, Cohen’s d=0.13. However, the equivalence test was also not statistically significant, t(83) = -1.08, p=.14. We therefore could not reject the null hypothesis that the absolute effect size was at least as large as d=0.25.

#quick sanity check
#t-test in tost is equivalent to regular old paired t-test
# AND equivalent to lmer estimate of typicality effect
t.test(
  avg_corrected_target_looking_by_typicality$average_corrected_target_looking[avg_corrected_target_looking_by_typicality$condition=="typical"],
  avg_corrected_target_looking_by_typicality$average_corrected_target_looking[avg_corrected_target_looking_by_typicality$condition=="atypical"], 
  paired=T)

## 
##  Paired t-test
## 
## data:  avg_corrected_target_looking_by_typicality$average_corrected_target_looking[avg_corrected_target_looking_by_typicality$condition == "typical"] and avg_corrected_target_looking_by_typicality$average_corrected_target_looking[avg_corrected_target_looking_by_typicality$condition == "atypical"]
## t = 1.2078, df = 83, p-value = 0.2305
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -0.009522991  0.038972172
## sample estimates:
## mean difference 
##      0.01472459

#effect size
cohens_d(avg_corrected_target_looking_by_typicality$average_corrected_target_looking[avg_corrected_target_looking_by_typicality$condition=="typical"],
         avg_corrected_target_looking_by_typicality$average_corrected_target_looking[avg_corrected_target_looking_by_typicality$condition=="atypical"],
         paired=T)

## Cohen's d |        95% CI
## -------------------------
## 0.13      | [-0.08, 0.35]

1.1.3

## Typical word recognition
# recentering the model on the typical condition to make the intercept interpretable
m_1_1_3_typ <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_typ + (1+ typicality_condition_typ|sub_num),data=avg_corrected_target_looking_by_typicality,control=lmerControl(check.nobs.vs.nlev= "ignore",check.nobs.vs.nRE= "ignore"))

summary(m_1_1_3_typ)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_corrected_target_looking ~ 1 + typicality_condition_typ +  
##     (1 + typicality_condition_typ | sub_num)
##    Data: avg_corrected_target_looking_by_typicality
## Control: 
## lmerControl(check.nobs.vs.nlev = "ignore", check.nobs.vs.nRE = "ignore")
## 
## REML criterion at convergence: -310.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.4304 -0.4351  0.0584  0.4481  2.0743 
## 
## Random effects:
##  Groups   Name                     Variance Std.Dev. Corr
##  sub_num  (Intercept)              0.005144 0.07172      
##           typicality_condition_typ 0.002461 0.04960  0.66
##  Residual                          0.005012 0.07079      
## Number of obs: 168, groups:  sub_num, 84
## 
## Fixed effects:
##                          Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)               0.07951    0.01100 83.00124   7.231 2.16e-10 ***
## typicality_condition_typ  0.01472    0.01219 83.00076   1.208    0.231    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.652

confint(m_1_1_3_typ,method="Wald")

##                                 2.5 %     97.5 %
## .sig01                             NA         NA
## .sig02                             NA         NA
## .sig03                             NA         NA
## .sigma                             NA         NA
## (Intercept)               0.057958346 0.10106071
## typicality_condition_typ -0.009169479 0.03861866

#effect size
cohens_d(avg_corrected_target_looking_by_typicality$average_corrected_target_looking[avg_corrected_target_looking_by_typicality$condition=="typical"])

## Cohen's d |       95% CI
## ------------------------
## 0.79      | [0.54, 1.03]

## Atypical word recognition
# recentering the model on the atypical condition to make the intercept interpretable
m_1_1_3_atyp <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_atyp + (1+ typicality_condition_atyp|sub_num),data=avg_corrected_target_looking_by_typicality,control=lmerControl(check.nobs.vs.nlev= "ignore",check.nobs.vs.nRE= "ignore"))

summary(m_1_1_3_atyp)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_corrected_target_looking ~ 1 + typicality_condition_atyp +  
##     (1 + typicality_condition_atyp | sub_num)
##    Data: avg_corrected_target_looking_by_typicality
## Control: 
## lmerControl(check.nobs.vs.nlev = "ignore", check.nobs.vs.nRE = "ignore")
## 
## REML criterion at convergence: -310.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.3225 -0.4158  0.0558  0.4281  1.9821 
## 
## Random effects:
##  Groups   Name                      Variance Std.Dev. Corr 
##  sub_num  (Intercept)               0.003375 0.05809       
##           typicality_condition_atyp 0.003332 0.05772  -0.17
##  Residual                           0.004576 0.06765       
## Number of obs: 168, groups:  sub_num, 84
## 
## Fixed effects:
##                            Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)                0.064785   0.009729 82.999758   6.659  2.8e-09 ***
## typicality_condition_atyp  0.014725   0.012191 83.000079   1.208    0.231    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ -0.516
## optimizer (nloptwrap) convergence code: 0 (OK)
## unable to evaluate scaled gradient
## Model failed to converge: degenerate  Hessian with 1 negative eigenvalues

confint(m_1_1_3_atyp,method="Wald")

##                                  2.5 %     97.5 %
## .sig01                              NA         NA
## .sig02                              NA         NA
## .sig03                              NA         NA
## .sigma                              NA         NA
## (Intercept)                0.045716306 0.08385357
## typicality_condition_atyp -0.009169478 0.03861866

#effect size
cohens_d(avg_corrected_target_looking_by_typicality$average_corrected_target_looking[avg_corrected_target_looking_by_typicality$condition=="atypical"])

## Cohen's d |       95% CI
## ------------------------
## 0.73      | [0.48, 0.97]

Infants robustly recognized the target words for both typical (Model: b=0.08, 95% CI [0.06, 0.10], t(83)=7.23, p<.001; Cohen’s d = 0.79 [0.54, 1.03]; Mean baseline-corrected looking: M=8.0%, 95% CI [5.8%, 10.1%]) and atypical exemplars (Model: b=0.06, 95% CI [0.05, 0.08], t(83)=6.66, p<.001, Cohen’s d = 0.73 [0.48, 0.97]; Mean baseline-corrected looking: M=6.5%, 95% CI [4.5%, 8.4%]).

1.2

trial_corrected_accuracy <- trial_corrected_accuracy %>%
  mutate(
    typicality_condition_c = case_when(
      condition == "atypical" ~ -0.5,
      condition == "typical" ~ 0.5,
      TRUE ~ NA_real_
    ),
    typicality_condition_typ = case_when(
      condition == "atypical" ~ -1,
      condition == "typical" ~ 0,
      TRUE ~ NA_real_
    ),
    typicality_condition_atyp = case_when(
      condition == "atypical" ~ 0,
      condition == "typical" ~ 1,
      TRUE ~ NA_real_
    ),
  )

#model with typicality condition yields a singular fit, so we removed the random slope
# however, the singular model still yields relatively identical results to the model
# without the typicality condition random slope
# m_1_2 <- lmer(corrected_target_looking ~ 1 + typicality_condition_c + 
#             (1 + typicality_condition_c|sub_num) +
#             (1|target_category),
#           data=trial_corrected_accuracy)

m_1_2 <- lmer(corrected_target_looking ~ 1 + typicality_condition_c + 
            (1 | sub_num) +
            (1|target_category),
          data=trial_corrected_accuracy)
summary(m_1_2)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking ~ 1 + typicality_condition_c + (1 |  
##     sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy
## 
## REML criterion at convergence: 2247.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.1618 -0.6169 -0.0213  0.6652  2.7744 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0028069 0.05298 
##  target_category (Intercept) 0.0002506 0.01583 
##  Residual                    0.1185987 0.34438 
## Number of obs: 3088, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                         Estimate Std. Error        df t value Pr(>|t|)   
## (Intercept)            7.297e-02  1.163e-02 5.248e+00   6.276  0.00126 **
## typicality_condition_c 1.080e-02  1.241e-02 3.017e+03   0.870  0.38412   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.000

confint(m_1_2,method="Wald")

##                              2.5 %     97.5 %
## .sig01                          NA         NA
## .sig02                          NA         NA
## .sigma                          NA         NA
## (Intercept)             0.05017938 0.09575134
## typicality_condition_c -0.01351946 0.03512238

#Centering on typical condition
m_1_2_typ <- lmer(corrected_target_looking ~ 1 + typicality_condition_typ + 
            (1 |sub_num) +
            (1|target_category),
          data=trial_corrected_accuracy)
summary(m_1_2_typ)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking ~ 1 + typicality_condition_typ + (1 |  
##     sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy
## 
## REML criterion at convergence: 2247.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.1618 -0.6169 -0.0213  0.6652  2.7744 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0028069 0.05298 
##  target_category (Intercept) 0.0002506 0.01583 
##  Residual                    0.1185987 0.34438 
## Number of obs: 3088, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                           Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)              7.837e-02  1.318e-02 8.665e+00   5.947 0.000251 ***
## typicality_condition_typ 1.080e-02  1.241e-02 3.017e+03   0.870 0.384116    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.471

confint(m_1_2_typ,method="Wald")

##                                2.5 %     97.5 %
## .sig01                            NA         NA
## .sig02                            NA         NA
## .sigma                            NA         NA
## (Intercept)               0.05253765 0.10419453
## typicality_condition_typ -0.01351946 0.03512238

#Centering on atypical condition
m_1_2_atyp <- lmer(corrected_target_looking ~ 1 + typicality_condition_atyp + 
            (1 |sub_num) +
            (1|target_category),
          data=trial_corrected_accuracy)
summary(m_1_2_atyp)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking ~ 1 + typicality_condition_atyp + (1 |  
##     sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy
## 
## REML criterion at convergence: 2247.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.1618 -0.6169 -0.0213  0.6652  2.7744 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0028069 0.05298 
##  target_category (Intercept) 0.0002506 0.01583 
##  Residual                    0.1185987 0.34438 
## Number of obs: 3088, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                            Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)               6.756e-02  1.318e-02 8.662e+00   5.127 0.000701 ***
## typicality_condition_atyp 1.080e-02  1.241e-02 3.017e+03   0.870 0.384116    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ -0.471

confint(m_1_2_atyp,method="Wald")

##                                 2.5 %     97.5 %
## .sig01                             NA         NA
## .sig02                             NA         NA
## .sigma                             NA         NA
## (Intercept)                0.04173737 0.09339188
## typicality_condition_atyp -0.01351946 0.03512238

The model with the maximal random effects structure yielded a singular fit that was only remedied by removing the by-participant random slope for typicality condition. However, the (singular) model including the typicality random slope yielded virtually identical results to the converging model including random intercepts for participant and target word only. As in the average participant-level analysis, infants’ overall recognition of target words was significant in the trial-level model (b=0.07, 95% CI [0.05,0.10], t(5.2)=6.28, p=.001) and there was no significant effect of typicality (b=0.01, 95% CI [-0.01,0.04], t(3017)=0.87, p=.38). Word recognition was robust both for typical (b=0.08, 95% CI [0.05,0.10], t(8.7)=5.95, p<.001) and atypical exemplars (b=0.07, 95% CI [0.04,0.9], t(8.7)=5.13, p<.001).

1.3

The cluster-based permutation analysis is executed in cluster_permutation_analysis.Rmd.

In the cluster-based permutation analyses, we found one cluster of adjacent time bins ranging from 0-300ms with |t|>2 (in the direction of higher accuracy for typical exemplars compared to atypical exemplars). However, this cluster did not reach significance in the permutation test, p=.27.

Timecourse Plots

Overall

Next, we plot the data. First we summarize the data in two steps: (1) summarize the data by subject for each time point, followed by (2) averaging looking for each time point across subjects.

#summarizing within subject for each time point
summarize_subj <- d_resampled %>%
  filter(exclude_participant==0) %>%
  filter(useable_window==1) %>%
  group_by(sub_num, child_gender, time_normalized_corrected) %>%
  summarize(N=n(),
            mean_age=mean(age),
            mean_age_mo=mean(age_mo),
            non_na_n = sum(!is.na(accuracy_transformed)), 
            mean_accuracy=mean(accuracy_transformed,na.rm=TRUE),
            ci=qt(0.975, non_na_n-1)*sd(accuracy_transformed,na.rm=T)/sqrt(non_na_n),
            lower_ci=mean_accuracy-ci,
            upper_ci=mean_accuracy+ci) %>%
  ungroup()

#summarizing across subjects for each time point
summarize_across_subj <- summarize_subj %>%
  group_by(time_normalized_corrected) %>%
  dplyr::summarize(n=n(),
            accuracy=mean(mean_accuracy,na.rm=TRUE),
            sd_accuracy=sd(mean_accuracy,na.rm=TRUE),
            se_accuracy=sd_accuracy/sqrt(n))

ggplot(summarize_across_subj,aes(time_normalized_corrected,accuracy))+
  xlim(-2000,4000)+
  geom_smooth(method="gam")+
  geom_errorbar(aes(ymin=accuracy-se_accuracy,ymax=accuracy+se_accuracy),width=0)+
  geom_point()+
  geom_vline(xintercept=0,size=1.5)+
  geom_hline(yintercept=0.5,size=1.2,linetype="dashed")+
  geom_vline(xintercept=300,linetype="dotted")+
  ylim(0.35,0.65)+
  xlab("Time (normalized to target word onset) in ms")+
  ylab("Proportion Target Looking")

ggsave(here::here("..","figures","overall_accuracy.png"))

Timecourse by age

summarize_across_subj_by_age <- summarize_subj %>%
  mutate(age_group=cut_number(mean_age_mo,n=4)) %>%
  group_by(age_group,time_normalized_corrected) %>%
  dplyr::summarize(n=n(),
                   accuracy=mean(mean_accuracy,na.rm=TRUE),
                   sd_accuracy=sd(mean_accuracy,na.rm=TRUE),
                   se_accuracy=sd_accuracy/sqrt(n))
ggplot(summarize_across_subj_by_age,aes(time_normalized_corrected,accuracy))+
  xlim(-2000,4000)+
  geom_smooth(method="gam")+
  geom_errorbar(aes(ymin=accuracy-se_accuracy,ymax=accuracy+se_accuracy),width=0)+
  geom_point()+
  geom_vline(xintercept=0,size=1.5)+
  geom_hline(yintercept=0.5,size=1.2,linetype="dashed")+
  geom_vline(xintercept=300,linetype="dotted")+
  facet_wrap(~age_group)+
  xlab("Time (normalized to target word onset) in ms")+
  ylab("Proportion Target Looking")

ggsave(here::here("..","figures","overall_accuracy_by_age.png"),width=12, height=9)

Timecourse by condition

summarize_subj_condition <- d_resampled %>%
  filter(exclude_participant==0) %>%
  filter(useable_window==1) %>%
  group_by(sub_num, child_gender, condition, time_normalized_corrected) %>%
  summarize(
    mean_age=mean(age),
    mean_age_mo=mean(age_mo),
    mean_accuracy=mean(accuracy_transformed,na.rm=TRUE))

summarize_across_subj_cond <- summarize_subj_condition %>%
  group_by(condition,time_normalized_corrected) %>%
  summarize(n=n(),
            accuracy=mean(mean_accuracy,na.rm=TRUE),
            sd_accuracy=sd(mean_accuracy,na.rm=TRUE),
            se_accuracy=sd_accuracy/sqrt(n))

#plot
#timecourse plot
pal <- wes_palette("Rushmore1", n=5)
timecourse_plot <- ggplot(summarize_across_subj_cond,aes(time_normalized_corrected,accuracy,color=condition))+
  geom_rect(data = data.frame(xmin = 300,
                              xmax = 2800,
                              ymin = -Inf,
                              ymax = Inf),
            aes(x=NULL, y=NULL,xmin = xmin, xmax = xmax, ymin = ymin, ymax = ymax,color=NULL),
            fill = "grey", alpha = 0.2)+
  geom_rect(data = data.frame(xmin = -2000,
                              xmax = 0,
                              ymin = -Inf,
                              ymax = Inf),
            aes(x=NULL, y=NULL,xmin = xmin, xmax = xmax, ymin = ymin, ymax = ymax,color=NULL),
            fill = "grey", alpha = 0.2)+
  geom_errorbar(aes(ymin=accuracy-se_accuracy,ymax=accuracy+se_accuracy),width=0)+
  geom_point(alpha=0.5)+
  geom_smooth(data=summarize_subj_condition,aes(y=mean_accuracy),method="gam")+
  geom_vline(xintercept=0,size=1.5)+
  geom_hline(yintercept=0.5,size=1.2,linetype="dashed")+
  geom_vline(xintercept=300,linetype="dotted")+
  geom_vline(xintercept=2800,linetype="dotted")+
  geom_vline(xintercept=-2000,linetype="dotted")+
  geom_vline(xintercept=0,linetype="dotted")+
  theme(legend.position = c(0.8,0.15))+
  annotate("text",label="Critical Window",x=1550,y=0.9,size=6)+
  annotate("text",label="Baseline Window",x=-1000,y=0.9,size=6)+
  ylim(0,1)+
  #xlim(-2000,4000)+
  scale_x_continuous(breaks=seq(-2000,4000,1000),limits=c(-2000,4000))+
  scale_colour_manual(values=pal[c(3,4)])+
  ylab("Proportion Target Looking")+
  xlab("Time (centered on target word onset, in ms)")+
  theme(
    strip.background = element_rect(size=1, colour = "black"),
    strip.text = element_text(size=16,face="bold"),
    axis.title=element_text(size=20,face="bold"),
    axis.text = element_text(size=14),
    legend.text=element_text(size=18),
    legend.title=element_text(size=18))
ggsave(here::here("..","figures","typicality_accuracy.png"),width=10,height=6)

Aim 2

Linear mixed-effects model

#join in average age-centered variables
trial_corrected_accuracy <- trial_corrected_accuracy %>%
  left_join(subj_info_multisession)
  
#fit main model
# the random slope of typicality causes a singular boundary fit
# all attempts to prune other random effects (including covariances) were not successful,
# so we removed the random slope for typicality.
# Note that the effects for the (singular fit) model including the random slope for typicality are 
# equivalent to the model with typicality condition as a random slope.
m_2 <- lmer(corrected_target_looking ~ 1 + typicality_condition_c * age_mo_c + 
            (1|sub_num) +
            (1|target_category),
          data=trial_corrected_accuracy)

summary(m_2)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking ~ 1 + typicality_condition_c * age_mo_c +  
##     (1 | sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy
## 
## REML criterion at convergence: 2252.8
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -3.13164 -0.63461 -0.02025  0.66770  2.80638 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0021621 0.04650 
##  target_category (Intercept) 0.0002606 0.01614 
##  Residual                    0.1186060 0.34439 
## Number of obs: 3088, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                                  Estimate Std. Error        df t value Pr(>|t|)
## (Intercept)                     7.258e-02  1.140e-02 4.644e+00   6.367  0.00185
## typicality_condition_c          1.062e-02  1.242e-02 3.018e+03   0.855  0.39251
## age_mo_c                        1.806e-02  5.415e-03 8.871e+01   3.336  0.00124
## typicality_condition_c:age_mo_c 5.710e-03  8.413e-03 3.017e+03   0.679  0.49741
##                                   
## (Intercept)                     **
## typicality_condition_c            
## age_mo_c                        **
## typicality_condition_c:age_mo_c   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) typc__ ag_m_c
## typclty_cn_  0.000              
## age_mo_c    -0.016  0.005       
## typclt__:__  0.004 -0.034  0.000

confint(m_2,method="Wald")

##                                        2.5 %     97.5 %
## .sig01                                    NA         NA
## .sig02                                    NA         NA
## .sigma                                    NA         NA
## (Intercept)                      0.050236937 0.09491934
## typicality_condition_c          -0.013715660 0.03495001
## age_mo_c                         0.007450156 0.02867635
## typicality_condition_c:age_mo_c -0.010779703 0.02219878

#save interim model object
m_2_tidy <- m_2 %>%
  summarize_mixed_effects_model()

In the trial-level linear mixed-effects model including age, typicality condition, and their interaction, we found a significant effect of age (\(\hat{\beta} = 0.02\), 95% CI \([0.01, 0.03]\), \(t(88.71) = 3.34\), \(p = .001\)), suggesting that word recognition accuracy increased with age overall. There was no significant interaction between age and typicality (\(\hat{\beta} = 0.01\), 95% CI \([-0.01, 0.02]\), \(t(3,016.88) = 0.68\), \(p = .497\)), meaning that we found no evidence that the effect of typicality changed with age.

Plot

Overall

ggplot(avg_corrected_target_looking,aes(mean_age,average_corrected_target_looking))+
  geom_pointrange(aes(ymin=lower_ci,ymax=upper_ci),
                  position=position_jitter(width=0.1),
                  width=0,
                  size=1.5) +
  geom_hline(yintercept=0,linetype="dashed")+
  geom_smooth(method="lm")+
  xlab("Age (in months)")+
  ylab("Baseline-Corrected Proportion Target Looking")+
  ylim(-0.55,0.55)+
  scale_x_continuous(breaks=seq(12,18,1))

ggsave(here::here("..","figures","age_relationship_baseline_corrected_accuracy.png"),width=7,height=6)

By Condition

pal <- wes_palette("Rushmore1", n=5)
p1 <- ggplot(avg_corrected_target_looking_by_typicality,aes(mean_age_mo,average_corrected_target_looking,color=condition,group=condition))+
  geom_pointrange(aes(ymin=lower_se,ymax=upper_se), 
                  position=position_jitter(width=0.2),
                  width=0,
                  size=1) +
  geom_hline(yintercept=0,linetype="dashed")+
  geom_smooth(method="lm",color="black",size=1.3)+
  xlab("Age (in months)")+
  ylab("Baseline-Corrected\nProportion Target Looking")+
  #ylim(-0.55,0.5)+
  scale_colour_manual(values=pal[c(3,4)])+
  scale_x_continuous(breaks=seq(12,18,1))+
  facet_wrap(~condition)+
  theme(
    strip.background = element_rect(size=1, colour = "black"),
    strip.text = element_text(size=16,face="bold"),
    axis.title=element_text(size=20,face="bold"),
    axis.text = element_text(size=14))+
  theme(legend.position="none")
ggsave(here::here("..","figures","age_relationship_baseline_corrected_accuracy_typicality.png"),width=9,height=6)

#combine key plots into one main figure
library(patchwork)

(p0 + p1) / timecourse_plot + 
  plot_annotation(tag_levels = 'A')+
  theme(plot.tag = element_text(size = 18))

ggsave(here::here("..","figures","main_figure.png"),width=12,height=12)

Aim 3

To test whether individual differences in word recognition or typicality effects are predicted by differences in experiences with each exemplar.

#subject details for aim 3 analysis (how many participants have survey data)
aim3_subject_info <- trial_corrected_accuracy %>%
  filter(!is.na(target_parent_typicality_rating_z)) %>%
  ungroup()%>%
  summarize(
    N = length(unique(sub_num)),
    mean_age = mean(age_c),
    sd_age = sd(age_c)
  )

aim3_subject_info%>%
  knitr::kable()

N	mean_age	sd_age
74	-0.7330562	45.0664

#fit main model
# as before, the random slope of typicality (this time parent-rated typicality) causes a singular boundary fit
# all attempts to prune other random effects (including covariances) were not successful,
# so we removed the random slope for target_parent_typicality_rating_z.
# Note that the effects for the (singular fit) model including the random slope for typicality are 
# equivalent to the model with typicality as a random slope.
# In other words, the decision to omit the random slope does not substantively impact the main estimates or change the pattern of results
# m_3 <- lmer(corrected_target_looking ~ 1 + target_parent_typicality_rating_z + age_mo_c + (1+ target_parent_typicality_rating_z|sub_num) + (1|target_category), trial_corrected_accuracy)
m_3 <- lmer(corrected_target_looking ~ 1 + target_parent_typicality_rating_z + age_mo_c + (1|sub_num) + (1|target_category), trial_corrected_accuracy)

summary(m_3)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking ~ 1 + target_parent_typicality_rating_z +  
##     age_mo_c + (1 | sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy
## 
## REML criterion at convergence: 1995.6
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -3.11217 -0.63232 -0.02323  0.66553  2.77341 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0024417 0.04941 
##  target_category (Intercept) 0.0003568 0.01889 
##  Residual                    0.1196135 0.34585 
## Number of obs: 2702, groups:  sub_num, 74; target_category, 4
## 
## Fixed effects:
##                                    Estimate Std. Error        df t value
## (Intercept)                       7.239e-02  1.295e-02 4.658e+00   5.589
## target_parent_typicality_rating_z 4.967e-03  6.871e-03 2.323e+03   0.723
## age_mo_c                          1.475e-02  5.956e-03 6.716e+01   2.477
##                                   Pr(>|t|)   
## (Intercept)                        0.00316 **
## target_parent_typicality_rating_z  0.46984   
## age_mo_c                           0.01577 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) tr____
## trgt_prn___ 0.008        
## age_mo_c    0.025  0.012

m_3_tidy <- m_3 %>%
  summarize_mixed_effects_model()

Caregiver report of exemplar typicality did not significantly predict infants’ baseline-corrected word recognition accuracy (\(\hat{\beta} = 0.00\), 95% CI \([-0.01, 0.02]\), \(t(2,322.50) = 0.72\), \(p = .470\)). Controlling for parent-reported typicality, age remained a significant predictor of infants’ word recognition (\(\hat{\beta} = 0.01\), 95% CI \([0.00, 0.03]\), \(t(67.16) = 2.48\), \(p = .016\)).

Visualization

#quick visualization of the (non-)effect for each category
#by category
ggplot(trial_corrected_accuracy,aes(target_parent_typicality_rating_z,corrected_target_looking))+
  geom_point(alpha=0.1)+
  geom_smooth(method = "lm")+
  facet_wrap(~target_category)

4. Robustness Analyses

We also conducted a series of robustness analyses to probe the degree to which any results hinged on key analytic decisions.

4.1. Window Choice

Summarize data

We conducted the same main analyses as those described above using an alternative, shorter critical window of 300-1800ms (e.g., Fernald et al., 2008) (with the exception of the cluster-based permutation analysis described in analysis section 1.3).

First, we summarize participants looking behavior as before, using the new critical window.

# apply exclusions based on the new critical window
trial_corrected_accuracy_short_window <- trial_corrected_accuracy_all %>%
  filter(exclude_participant_insufficient_data_short==0) %>%
  #only include trials that are useable based on looking in the 300-1800ms window
  filter(useable_window_short==1) %>%
  #ignore trial exclusions due to "insufficient looking" based on 300-2800ms window
  filter(is.na(trial_exclusion_reason) | trial_exclusion_reason=="insufficient looking")

# summarize average accuracy within participant, split by typicality
avg_corrected_target_looking_by_typicality_short_window <- trial_corrected_accuracy_short_window  %>%
  group_by(sub_num, condition) %>%
  summarize(N=n(),
            mean_age = mean(age),
            mean_age_mo = mean(age_mo),
            average_corrected_target_looking=mean(corrected_target_looking_short,na.rm=TRUE),
            se=sd(corrected_target_looking_short,na.rm=T)/sqrt(N),
            ci=qt(0.975, N-1)*sd(corrected_target_looking_short,na.rm=T)/sqrt(N),
            lower_ci=average_corrected_target_looking-ci,
            upper_ci=average_corrected_target_looking+ci,
            lower_se=average_corrected_target_looking-se,
            upper_se=average_corrected_target_looking+se)

#baseline-corrected target looking summarized overall
overall_corrected_target_looking_by_typicality_short_window <- avg_corrected_target_looking_by_typicality_short_window %>%
  group_by(condition) %>%
  summarize(N=n(),
            corrected_target_looking=mean(average_corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(average_corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=corrected_target_looking-ci,
            upper_ci=corrected_target_looking+ci)

overall_corrected_target_looking_by_typicality_short_window %>%
  knitr::kable()

condition	N	corrected_target_looking	ci	lower_ci	upper_ci
atypical	82	0.0574887	0.0213794	0.0361094	0.0788681
typical	82	0.0780616	0.0220918	0.0559697	0.1001534

Participant-level analysis

Aim 1.1

#1.1. Participant-level analysis of the typicality effect
avg_corrected_target_looking_by_typicality_short_window <- avg_corrected_target_looking_by_typicality_short_window %>%
  mutate(
    typicality_condition_c = case_when(
      condition == "atypical" ~ -0.5,
      condition == "typical" ~ 0.5,
      TRUE ~ NA_real_
    ),
    typicality_condition_typ = case_when(
      condition == "atypical" ~ -1,
      condition == "typical" ~ 0,
      TRUE ~ NA_real_
    ),
    typicality_condition_atyp = case_when(
      condition == "atypical" ~ 0,
      condition == "typical" ~ 1,
      TRUE ~ NA_real_
    ),
  )

m_4_1_1_1 <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_c + (1+ typicality_condition_c|sub_num),data=avg_corrected_target_looking_by_typicality_short_window,control=lmerControl(check.nobs.vs.nlev= "ignore",check.nobs.vs.nRE= "ignore"))

summary(m_4_1_1_1)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_corrected_target_looking ~ 1 + typicality_condition_c +  
##     (1 + typicality_condition_c | sub_num)
##    Data: avg_corrected_target_looking_by_typicality_short_window
## Control: 
## lmerControl(check.nobs.vs.nlev = "ignore", check.nobs.vs.nRE = "ignore")
## 
## REML criterion at convergence: -284.2
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -1.91157 -0.34766  0.09098  0.42244  1.26530 
## 
## Random effects:
##  Groups   Name                   Variance Std.Dev. Corr
##  sub_num  (Intercept)            0.004173 0.06460      
##           typicality_condition_c 0.009034 0.09505  0.05
##  Residual                        0.003357 0.05794      
## Number of obs: 164, groups:  sub_num, 82
## 
## Fixed effects:
##                         Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)             0.067775   0.008447 80.998673   8.023 6.76e-12 ***
## typicality_condition_c  0.020573   0.013858 81.000990   1.485    0.142    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.033 
## optimizer (nloptwrap) convergence code: 0 (OK)
## unable to evaluate scaled gradient
## Model failed to converge: degenerate  Hessian with 1 negative eigenvalues

confint(m_4_1_1_1,method="Wald")

##                               2.5 %     97.5 %
## .sig01                           NA         NA
## .sig02                           NA         NA
## .sig03                           NA         NA
## .sigma                           NA         NA
## (Intercept)             0.051218712 0.08433158
## typicality_condition_c -0.006588576 0.04773425

#effect size
cohens_d(
  filter(avg_corrected_target_looking_by_typicality_short_window,condition=="typical")$average_corrected_target_looking,
  filter(avg_corrected_target_looking_by_typicality_short_window,condition=="atypical")$average_corrected_target_looking,
  paired=T)

## Cohen's d |        95% CI
## -------------------------
## 0.16      | [-0.05, 0.38]

There was no significant effect of typicality in the average participant-level analysis, b=0.02, 95% CI [-0.007, 0.05], t(81)=1.49, p=.14, Cohen’s d=0.16 [-0.05, 0.38].

# run equivalence test
overall_condition_summary_short_window <- avg_corrected_target_looking_by_typicality_short_window %>%
  group_by(sub_num) %>%
  summarize(
    condition_diff_alternative = average_corrected_target_looking[condition=="typical"]-average_corrected_target_looking[condition=="atypical"]
  ) %>%
  ungroup() %>%
  summarize(
    N=n(),
    diff = mean(condition_diff_alternative),
    sd = sd(condition_diff_alternative)
  )

tsum_TOST(m1=overall_condition_summary_short_window$diff,sd1=overall_condition_summary_short_window$sd,n1=overall_condition_summary_short_window$N,eqb=0.25, eqbound_type = "SMD")

## 
## One-sample t-Test
## 
## The equivalence test was non-significant, t(81) = -0.779, p = 2.19e-01
## The null hypothesis test was non-significant, t(81) = 1.485, p = 1.42e-01
## NHST: don't reject null significance hypothesis that the effect is equal to zero 
## TOST: don't reject null equivalence hypothesis
## 
## TOST Results 
##                  t df p.value
## t-test      1.4845 81   0.142
## TOST Lower  3.7484 81 < 0.001
## TOST Upper -0.7793 81   0.219
## 
## Effect Sizes 
##            Estimate      SE              C.I. Conf. Level
## Raw         0.02057 0.01386 [-0.0025, 0.0436]         0.9
## Hedges's g  0.16241 0.11116 [-0.0193, 0.3431]         0.9
## Note: SMD confidence intervals are an approximation. See vignette("SMD_calcs").

As in the main analysis, the equivalence test was also not significant, t(81)=-0.78, p=.22.

#word recognition for typical items
m_1_1_3_typ_short_window <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_typ + (1+ typicality_condition_typ|sub_num),data=avg_corrected_target_looking_by_typicality_short_window,control=lmerControl(check.nobs.vs.nlev= "ignore",check.nobs.vs.nRE= "ignore"))
summary(m_1_1_3_typ_short_window)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_corrected_target_looking ~ 1 + typicality_condition_typ +  
##     (1 + typicality_condition_typ | sub_num)
##    Data: avg_corrected_target_looking_by_typicality_short_window
## Control: 
## lmerControl(check.nobs.vs.nlev = "ignore", check.nobs.vs.nRE = "ignore")
## 
## REML criterion at convergence: -284.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.3923 -0.4351  0.1139  0.5287  1.5835 
## 
## Random effects:
##  Groups   Name                     Variance Std.Dev. Corr
##  sub_num  (Intercept)              0.004851 0.06965      
##           typicality_condition_typ 0.005233 0.07234  0.58
##  Residual                          0.005258 0.07251      
## Number of obs: 164, groups:  sub_num, 82
## 
## Fixed effects:
##                          Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)               0.07806    0.01110 80.99961   7.031 5.89e-10 ***
## typicality_condition_typ  0.02057    0.01386 81.00018   1.485    0.142    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.649 
## optimizer (nloptwrap) convergence code: 0 (OK)
## unable to evaluate scaled gradient
## Model failed to converge: degenerate  Hessian with 1 negative eigenvalues

confint(m_1_1_3_typ_short_window,method="Wald")

##                                 2.5 %     97.5 %
## .sig01                             NA         NA
## .sig02                             NA         NA
## .sig03                             NA         NA
## .sigma                             NA         NA
## (Intercept)               0.056299711 0.09982341
## typicality_condition_typ -0.006588705 0.04773438

#effect size
cohens_d(avg_corrected_target_looking_by_typicality_short_window$average_corrected_target_looking[avg_corrected_target_looking_by_typicality_short_window$condition=="typical"])

## Cohen's d |       95% CI
## ------------------------
## 0.78      | [0.53, 1.02]

#word recognition for atypical items
m_1_1_3_atyp_short_window <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_atyp + (1+ typicality_condition_atyp|sub_num),data=avg_corrected_target_looking_by_typicality_short_window,control=lmerControl(check.nobs.vs.nlev= "ignore",check.nobs.vs.nRE= "ignore"))
summary(m_1_1_3_atyp_short_window)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_corrected_target_looking ~ 1 + typicality_condition_atyp +  
##     (1 + typicality_condition_atyp | sub_num)
##    Data: avg_corrected_target_looking_by_typicality_short_window
## Control: 
## lmerControl(check.nobs.vs.nlev = "ignore", check.nobs.vs.nRE = "ignore")
## 
## REML criterion at convergence: -284.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.3682 -0.4307  0.1127  0.5234  1.5675 
## 
## Random effects:
##  Groups   Name                      Variance Std.Dev. Corr 
##  sub_num  (Intercept)               0.004315 0.06569       
##           typicality_condition_atyp 0.005443 0.07378  -0.50
##  Residual                           0.005152 0.07178       
## Number of obs: 164, groups:  sub_num, 82
## 
## Fixed effects:
##                           Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)                0.05749    0.01075 80.99992   5.350 7.97e-07 ***
## typicality_condition_atyp  0.02057    0.01386 81.00009   1.485    0.142    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ -0.619
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model is nearly unidentifiable: large eigenvalue ratio
##  - Rescale variables?

confint(m_1_1_3_atyp_short_window,method="Wald")

##                                  2.5 %     97.5 %
## .sig01                              NA         NA
## .sig02                              NA         NA
## .sig03                              NA         NA
## .sigma                              NA         NA
## (Intercept)                0.036428719 0.07854873
## typicality_condition_atyp -0.006588751 0.04773443

#effect size
cohens_d(avg_corrected_target_looking_by_typicality_short_window$average_corrected_target_looking[avg_corrected_target_looking_by_typicality_short_window$condition=="atypical"])

## Cohen's d |       95% CI
## ------------------------
## 0.59      | [0.35, 0.82]

Infants showed robust recognition of both typical (b=0.08, 95% CI [0.06, 0.10], t(81)=7.03, p<.001, Cohen’s d=0.78 [0.53, 1.02]) and atypical targets (b=0.06, 95% CI [0.04, 0.08], t(81)=5.35, p<.001, Cohen’s d=0.59 [0.35, 0.82]).

Trial-level analyses (Aims 1.2, 2, and 3)

Aim 1.2.

# 1.2.
# trial-level analysis of the typicality effect
trial_corrected_accuracy_short_window <- trial_corrected_accuracy_short_window %>%
  mutate(
    typicality_condition_c = case_when(
      condition == "atypical" ~ -0.5,
      condition == "typical" ~ 0.5,
      TRUE ~ NA_real_
    ),
    typicality_condition_typ = case_when(
      condition == "atypical" ~ -1,
      condition == "typical" ~ 0,
      TRUE ~ NA_real_
    ),
    typicality_condition_atyp = case_when(
      condition == "atypical" ~ 0,
      condition == "typical" ~ 1,
      TRUE ~ NA_real_
    ),
  )

m_4_1_1_2 <- lmer(corrected_target_looking_short ~ 1 + typicality_condition_c + 
            (1 |sub_num) +
            (1|target_category),
          data=trial_corrected_accuracy_short_window)
summary(m_4_1_1_2)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking_short ~ 1 + typicality_condition_c +  
##     (1 | sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy_short_window
## 
## REML criterion at convergence: 3166.4
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.7188 -0.6977  0.0018  0.7387  2.4109 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0016953 0.04117 
##  target_category (Intercept) 0.0003626 0.01904 
##  Residual                    0.1622029 0.40274 
## Number of obs: 3066, groups:  sub_num, 82; target_category, 4
## 
## Fixed effects:
##                         Estimate Std. Error        df t value Pr(>|t|)   
## (Intercept)            6.930e-02  1.284e-02 3.891e+00   5.399  0.00616 **
## typicality_condition_c 1.546e-02  1.456e-02 2.999e+03   1.062  0.28821   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.001

confint(m_4_1_1_2,method="Wald")

##                              2.5 %     97.5 %
## .sig01                          NA         NA
## .sig02                          NA         NA
## .sigma                          NA         NA
## (Intercept)             0.04414589 0.09445940
## typicality_condition_c -0.01306713 0.04399158

We again found no significant effect of typicality (b=0.02, 95% CI [-0.01, 0.04], t(2999)=1.06, p=.29).

Aim 2

# Aim 2: Typicality by Age interaction
trial_corrected_accuracy_short_window <- trial_corrected_accuracy_short_window %>%
  left_join(subj_info_multisession)
  

m_4_1_2 <- lmer(corrected_target_looking_short ~ 1 + typicality_condition_c * age_mo_c + 
            (1|sub_num) +
            (1|target_category),
          data=trial_corrected_accuracy_short_window)
summary(m_4_1_2)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking_short ~ 1 + typicality_condition_c *  
##     age_mo_c + (1 | sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy_short_window
## 
## REML criterion at convergence: 3173.2
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.73731 -0.69913  0.00321  0.74213  2.44769 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0011751 0.03428 
##  target_category (Intercept) 0.0003739 0.01934 
##  Residual                    0.1622103 0.40275 
## Number of obs: 3066, groups:  sub_num, 82; target_category, 4
## 
## Fixed effects:
##                                  Estimate Std. Error        df t value Pr(>|t|)
## (Intercept)                     6.885e-02  1.269e-02 3.590e+00   5.424  0.00760
## typicality_condition_c          1.526e-02  1.456e-02 2.999e+03   1.048  0.29471
## age_mo_c                        1.679e-02  5.616e-03 8.566e+01   2.989  0.00366
## typicality_condition_c:age_mo_c 6.881e-03  9.968e-03 2.997e+03   0.690  0.49005
##                                   
## (Intercept)                     **
## typicality_condition_c            
## age_mo_c                        **
## typicality_condition_c:age_mo_c   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) typc__ ag_m_c
## typclty_cn_  0.001              
## age_mo_c    -0.017  0.005       
## typclt__:__  0.003 -0.034 -0.001

confint(m_4_1_2,method="Wald")

##                                       2.5 %     97.5 %
## .sig01                                   NA         NA
## .sig02                                   NA         NA
## .sigma                                   NA         NA
## (Intercept)                      0.04396814 0.09372988
## typicality_condition_c          -0.01328057 0.04380545
## age_mo_c                         0.00577754 0.02779367
## typicality_condition_c:age_mo_c -0.01265606 0.02641858

As in the main analysis, we also found no interaction between age and typicality (Aim 2). Age remained a significant predictor of accuracy.

Aim 3

#Aim 3
#parent typicality ratings as a predictor
m_4_1_3 <- lmer(corrected_target_looking_short ~ 1 + target_parent_typicality_rating_z + age_mo_c + (1|sub_num) + (1|target_category), trial_corrected_accuracy_short_window)

summary(m_4_1_3)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## corrected_target_looking_short ~ 1 + target_parent_typicality_rating_z +  
##     age_mo_c + (1 | sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy_short_window
## 
## REML criterion at convergence: 2793.8
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.73384 -0.69325  0.00725  0.73690  2.48279 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0011102 0.03332 
##  target_category (Intercept) 0.0005681 0.02383 
##  Residual                    0.1627387 0.40341 
## Number of obs: 2693, groups:  sub_num, 72; target_category, 4
## 
## Fixed effects:
##                                    Estimate Std. Error        df t value
## (Intercept)                       7.137e-02  1.478e-02 3.448e+00   4.829
## target_parent_typicality_rating_z 1.036e-02  8.036e-03 2.372e+03   1.289
## age_mo_c                          1.555e-02  5.921e-03 6.875e+01   2.626
##                                   Pr(>|t|)  
## (Intercept)                         0.0122 *
## target_parent_typicality_rating_z   0.1974  
## age_mo_c                            0.0106 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) tr____
## trgt_prn___ 0.007        
## age_mo_c    0.009  0.011

m_4_1_3_tidy <- m_4_1_3 %>%
  summarize_mixed_effects_model()

Caregiver report of exemplar typicality did not significantly predict infants’ baseline-corrected word recognition accuracy (\(\hat{\beta} = 0.01\), 95% CI \([-0.01, 0.03]\), \(t(2,372.40) = 1.29\), \(p = .197\)). After controlling for the effect of parental report of typicality, age remained a significant predictor of infants’ word recognition (\(\hat{\beta} = 0.02\), 95% CI \([0.00, 0.03]\), \(t(68.75) = 2.63\), \(p = .011\)).

4.2 excluding unknown words

We were unable to conduct a robustness analysis excluding words marked as unknown by caregivers due to the omission of the MCDI during data collection.

4.3 Using reaction times as the main dependent measure

To assess the consistency of typicality effects across multiple indices of word recognition, we fit the main two models in Aim 1 (section 1.1 and 1.2 in the Analysis Plan), testing for a typicality effect at the participant level and at the trial level, using a second dependent measure: reaction time.

Load RT

Reaction times are computed using helper functions in the R scripts rt_helper.R and compute_rt.R.

Here, we load in the trial-by-trial reaction time data and join it with other trial properties.

#load RT data
rt_path <- here::here("..","..","data","processed_data","CATegories_exp2_RT_by_trial.csv")
d_rt <- read_csv(rt_path)

#get some other useful metadata and combine with the RT data
d_trial_level <- d %>%
  distinct(sub_num,session, trial_number,condition, age, age_mo, target_image, child_gender,target_category,exclude_technical_issue,exclude_frame_rate)
d_rt<- d_rt %>%
  left_join(d_trial_level)

#participants must contribute 4 typical and 4 atypical trials to be included in analysis
d_rt_subj_summary <- d_rt %>%
  #we only care about distractor-to-target shifts (not e.g. T-D, target-distractor shifts)
  filter(shift_type == "D-T")%>%
  #only include RTs within the critical window
  filter(rt>=300) %>%
  filter(rt<=2800) %>%
  #only include participants from the final sample
  filter(exclude_participant==0) %>%
  #exclude any trials with technical issues or frame rate issues
  filter(exclude_frame_rate==0) %>%
  filter(exclude_technical_issue==0) %>%
  group_by(sub_num, condition) %>%
  summarize(
    trials = n()
  ) %>%
  pivot_wider(names_from=condition,names_prefix="useable_rt_trials_",values_from=trials) %>%
  # only include participants with at least 4 reaction time trials of each type
  mutate(
    sufficient_rt_trials=case_when(
      is.na(useable_rt_trials_typical) ~ 0,
      is.na(useable_rt_trials_atypical) ~ 0,
      useable_rt_trials_typical>=4 & useable_rt_trials_atypical>=4 ~ 1,
      TRUE ~ 0)
  )

#add exclusionary criteria to DF
d_rt <- d_rt %>%
  left_join(d_rt_subj_summary)

#apply exclusions and store the final RT dataset to use in analyses
d_rt_final <- d_rt %>%
  filter(shift_type == "D-T")%>%
  #only include RTs within the critical window
  filter(rt>=300) %>%
  filter(rt<=2800) %>%
  #only include participants from the final sample
  filter(exclude_participant==0) %>%
  #exclude any trials with technical issues or frame rate issues
  filter(exclude_frame_rate==0) %>%
  filter(exclude_technical_issue==0) %>%
  filter(sufficient_rt_trials==1)

Visualization of RTs

hist(filter(d_rt_final)$rt)

#log-transofrm rt
d_rt_final <- d_rt_final %>%
  mutate(
    log_rt = log(rt),
    log_shift_start_rt=log(shift_start_rt)
  )

The data are right skewed, which is common for RTs. We will use log transformations in the subsequent models to account for the distribution of the data.

4.3.1 Participant-level analysis with RT as DV

#summarize reaction time by participant and condition
avg_subj_rt <- d_rt_final %>%
  group_by(sub_num, child_gender,condition) %>%
  summarize(N=n(),
            average_rt=mean(rt,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(rt,na.rm=T)/sqrt(N),
            lower_ci=average_rt-ci,
            upper_ci=average_rt+ci,
            average_log_rt=mean(log_rt,na.rm=TRUE),
            log_rt_ci=qt(0.975, N-1)*sd(log_rt,na.rm=T)/sqrt(N),
            lower_log_rt_ci=average_log_rt-log_rt_ci,
            upper_log_rt_ci=average_log_rt+log_rt_ci) %>%
  mutate(
    typicality_condition_c = case_when(
      condition == "atypical" ~ -0.5,
      condition == "typical" ~ 0.5,
      TRUE ~ NA_real_
    )
  )

#overall reaction times
overall_rt <- avg_subj_rt %>%
  group_by(condition) %>%
  summarize(N=n(),
            avg_rt=mean(average_rt,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(average_rt,na.rm=T)/sqrt(N),
            lower_ci=avg_rt-ci,
            upper_ci=avg_rt+ci)

overall_rt %>%
  knitr::kable()

condition	N	avg_rt	ci	lower_ci	upper_ci
atypical	73	912.4030	63.01259	849.3904	975.4156
typical	73	893.2222	53.76717	839.4550	946.9893

# participant-level model testing the typicality effect
m_4_3_1 <- lmer(average_log_rt ~ 1 + typicality_condition_c + (1|sub_num),data=avg_subj_rt)

summary(m_4_3_1)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_log_rt ~ 1 + typicality_condition_c + (1 | sub_num)
##    Data: avg_subj_rt
## 
## REML criterion at convergence: 8.5
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.31039 -0.59944  0.02166  0.54475  2.54113 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  sub_num  (Intercept) 0.02292  0.1514  
##  Residual             0.03991  0.1998  
## Number of obs: 146, groups:  sub_num, 73
## 
## Fixed effects:
##                        Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)             6.65188    0.02424 72.00000 274.466   <2e-16 ***
## typicality_condition_c -0.01262    0.03307 72.00000  -0.382    0.704    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.000

confint(m_4_3_1,method="Wald")

##                              2.5 %     97.5 %
## .sig01                          NA         NA
## .sigma                          NA         NA
## (Intercept)             6.60437915 6.69938141
## typicality_condition_c -0.07743288 0.05218727

4.3.2 Trial-level analysis with RT as DV

d_rt_final <- d_rt_final %>%
  mutate(
    typicality_condition_c = case_when(
      condition == "atypical" ~ -0.5,
      condition == "typical" ~ 0.5,
      TRUE ~ NA_real_
    )
  )

m_4_3_2 <- lmer(log_rt ~ 1 + typicality_condition_c + 
            (1|sub_num) +
            (1|target_category),
          data=d_rt_final)

summary(m_4_3_2)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## log_rt ~ 1 + typicality_condition_c + (1 | sub_num) + (1 | target_category)
##    Data: d_rt_final
## 
## REML criterion at convergence: 1704.1
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.06751 -0.69950 -0.04359  0.60787  2.46816 
## 
## Random effects:
##  Groups          Name        Variance Std.Dev.
##  sub_num         (Intercept) 0.01850  0.1360  
##  target_category (Intercept) 0.00243  0.0493  
##  Residual                    0.26711  0.5168  
## Number of obs: 1081, groups:  sub_num, 73; target_category, 4
## 
## Fixed effects:
##                          Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)               6.64235    0.03342    4.96794 198.750 6.97e-11 ***
## typicality_condition_c   -0.01232    0.03183 1042.52347  -0.387    0.699    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ -0.004

confint(m_4_3_2,method="Wald")

##                              2.5 %     97.5 %
## .sig01                          NA         NA
## .sig02                          NA         NA
## .sigma                          NA         NA
## (Intercept)             6.57684563 6.70785239
## typicality_condition_c -0.07469865 0.05005745

4.4 Testing whether effects interact with test session.

Given the multi-session structure of our data collection procedure, we also tested whether analyses held individually in each test session, by repeating the analyses above while including an interaction with test session (session 1 vs. session 2).

# summarize participants' overall average accuracy by session
avg_corrected_target_looking_by_session <- trial_corrected_accuracy  %>%
  group_by(sub_num,session,age,age_mo,days_between_sessions) %>%
  summarize(N=n(),
            mean_age = mean(age),
            mean_age_mo = mean(age_mo),
            average_corrected_target_looking=mean(corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=average_corrected_target_looking-ci,
            upper_ci=average_corrected_target_looking+ci)

# summarize average accuracy within participant, split by session and typicality
avg_corrected_target_looking_by_typicality_session <- trial_corrected_accuracy  %>%
  group_by(sub_num,session,age,age_mo,days_between_sessions, condition) %>%
  summarize(N=n(),
            average_corrected_target_looking=mean(corrected_target_looking,na.rm=TRUE),
            se=sd(corrected_target_looking,na.rm=T)/sqrt(N),
            ci=qt(0.975, N-1)*sd(corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=average_corrected_target_looking-ci,
            upper_ci=average_corrected_target_looking+ci,
            lower_se=average_corrected_target_looking-se,
            upper_se=average_corrected_target_looking+se,
            average_critical_window_looking=mean(mean_target_looking_critical,na.rm=TRUE),
            critical_window_ci = qt(0.975, N-1)*sd(mean_target_looking_critical,na.rm=T)/sqrt(N),
            critical_window_lower_ci=average_critical_window_looking-critical_window_ci,
            critical_window_upper_ci=average_critical_window_looking+critical_window_ci)

4.4.1. Participant-level analysis with test session interaction

avg_corrected_target_looking_by_typicality_session <- avg_corrected_target_looking_by_typicality_session %>%
  mutate(
    typicality_condition_c = case_when(
      condition == "atypical" ~ -0.5,
      condition == "typical" ~ 0.5,
      TRUE ~ NA_real_
    ),
    typicality_condition_typ = case_when(
      condition == "atypical" ~ -1,
      condition == "typical" ~ 0,
      TRUE ~ NA_real_
    ),
    typicality_condition_atyp = case_when(
      condition == "atypical" ~ 0,
      condition == "typical" ~ 1,
      TRUE ~ NA_real_
    ),    
    session_c = session - 1.5
  )

m_4_4_1 <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_c*session_c + (1+session_c|sub_num),data=avg_corrected_target_looking_by_typicality_session)

summary(m_4_4_1)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_corrected_target_looking ~ 1 + typicality_condition_c *  
##     session_c + (1 + session_c | sub_num)
##    Data: avg_corrected_target_looking_by_typicality_session
## 
## REML criterion at convergence: -393.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.9777 -0.6671 -0.0126  0.5817  3.2498 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  sub_num  (Intercept) 0.003352 0.05790       
##           session_c   0.003105 0.05572  -0.60
##  Residual             0.013120 0.11454       
## Number of obs: 327, groups:  sub_num, 84
## 
## Fixed effects:
##                                    Estimate Std. Error         df t value
## (Intercept)                        0.070725   0.008963  81.190001   7.891
## typicality_condition_c             0.017785   0.012677 155.822578   1.403
## session_c                          0.009662   0.014095  81.419191   0.686
## typicality_condition_c:session_c  -0.040695   0.025353 155.822579  -1.605
##                                  Pr(>|t|)    
## (Intercept)                      1.21e-11 ***
## typicality_condition_c              0.163    
## session_c                           0.495    
## typicality_condition_c:session_c    0.110    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) typc__ sssn_c
## typclty_cn_  0.003              
## session_c   -0.165 -0.003       
## typclty__:_ -0.003  0.021  0.003

confint(m_4_4_1,method="Wald")

##                                        2.5 %      97.5 %
## .sig01                                    NA          NA
## .sig02                                    NA          NA
## .sig03                                    NA          NA
## .sigma                                    NA          NA
## (Intercept)                       0.05315866 0.088291820
## typicality_condition_c           -0.00706130 0.042630647
## session_c                        -0.01796358 0.037287931
## typicality_condition_c:session_c -0.09038658 0.008997312

Below, we summarize participants’ average looking in the typical/atypical conditions by session

#baseline-corrected target looking summarized overall
overall_corrected_target_looking_by_typicality_session <- avg_corrected_target_looking_by_typicality_session %>%
  group_by(session,condition) %>%
  summarize(N=n(),
            corrected_target_looking=mean(average_corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(average_corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=corrected_target_looking-ci,
            upper_ci=corrected_target_looking+ci)

overall_corrected_target_looking_by_typicality_session %>%
  knitr::kable()

session	condition	N	corrected_target_looking	ci	lower_ci	upper_ci
1	atypical	84	0.0468282	0.0288367	0.0179915	0.0756648
1	typical	83	0.0869929	0.0313197	0.0556733	0.1183126
2	atypical	80	0.0765215	0.0272729	0.0492486	0.1037944
2	typical	80	0.0739589	0.0276708	0.0462881	0.1016297

4.4.2 Trial-level analysis with test session interaction

trial_corrected_accuracy <- trial_corrected_accuracy %>%
  mutate(
    session_c = session - 1.5
  )

m_4_4_2 <- lmer(corrected_target_looking ~ 1 + typicality_condition_c*session_c + 
            (1+session_c |sub_num) +
            (1|target_category),
          data=trial_corrected_accuracy)
summary(m_4_4_2)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking ~ 1 + typicality_condition_c * session_c +  
##     (1 + session_c | sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy
## 
## REML criterion at convergence: 2258.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.1876 -0.6206 -0.0278  0.6618  2.7884 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev. Corr 
##  sub_num         (Intercept) 0.0028156 0.05306       
##                  session_c   0.0001582 0.01258  -0.41
##  target_category (Intercept) 0.0002485 0.01576       
##  Residual                    0.1185757 0.34435       
## Number of obs: 3088, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                                    Estimate Std. Error         df t value
## (Intercept)                         0.07294    0.01161    5.27112   6.283
## typicality_condition_c              0.01110    0.01241 2945.59039   0.894
## session_c                           0.00293    0.01262   74.14827   0.232
## typicality_condition_c:session_c   -0.03065    0.02481 2949.11150  -1.236
##                                  Pr(>|t|)   
## (Intercept)                       0.00124 **
## typicality_condition_c            0.37123   
## session_c                         0.81698   
## typicality_condition_c:session_c  0.21670   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) typc__ sssn_c
## typclty_cn_  0.000              
## session_c   -0.033 -0.006       
## typclty__:_ -0.004 -0.020  0.001

confint(m_4_4_2,method="Wald")

##                                        2.5 %     97.5 %
## .sig01                                    NA         NA
## .sig02                                    NA         NA
## .sig03                                    NA         NA
## .sig04                                    NA         NA
## .sigma                                    NA         NA
## (Intercept)                       0.05018805 0.09569259
## typicality_condition_c           -0.01322543 0.03542345
## session_c                        -0.02179676 0.02765717
## typicality_condition_c:session_c -0.07927601 0.01796975

5. Exploratory analyses

5.1. Predicting average accuracy from continuous typicality ratings

Continuous typicality of target alone

Images were classified as typical vs. atypical based on an adult norming study. In this analysis, we investigated whether treating typicality as a continuous metric, using the norming ratings as a predictor, would provide us more power to detect a typicality effect.

m_5_1_1 <- lmer(corrected_target_looking ~ 1 + target_typicality_z + 
            (1|sub_num)+
              (1|target_category),
          data=trial_corrected_accuracy)
summary(m_5_1_1)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking ~ 1 + target_typicality_z + (1 | sub_num) +  
##     (1 | target_category)
##    Data: trial_corrected_accuracy
## 
## REML criterion at convergence: 2246.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.1798 -0.6232 -0.0247  0.6630  2.7694 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0028206 0.05311 
##  target_category (Intercept) 0.0002682 0.01638 
##  Residual                    0.1184828 0.34421 
## Number of obs: 3088, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                      Estimate Std. Error        df t value Pr(>|t|)   
## (Intercept)         7.304e-02  1.182e-02 5.159e+00    6.18  0.00145 **
## target_typicality_z 1.176e-02  6.354e-03 2.891e+03    1.85  0.06435 . 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## trgt_typcl_ 0.004

confint(m_5_1_1,method="Wald")

##                             2.5 %     97.5 %
## .sig01                         NA         NA
## .sig02                         NA         NA
## .sigma                         NA         NA
## (Intercept)          0.0498745657 0.09620693
## target_typicality_z -0.0006958822 0.02421020

Quick plot. Descriptively, it appears that perhaps there is a decrement in looking for items on the extreme end of typicality, and otherwise fairly similar target looking.

ggplot(trial_corrected_accuracy,aes(target_typicality_z,corrected_target_looking))+
  geom_point(aes(color=condition))+
  geom_hline(yintercept=0, linetype="dashed")+
  geom_smooth()

Continuous typicality of target AND distractor

m_5_1_2 <- lmer(corrected_target_looking ~ 1 + target_typicality_z + distractor_typicality_z+
            (1+target_typicality_z + distractor_typicality_z|sub_num)+
              (1|target_category),
          data=trial_corrected_accuracy)
summary(m_5_1_2)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## corrected_target_looking ~ 1 + target_typicality_z + distractor_typicality_z +  
##     (1 + target_typicality_z + distractor_typicality_z | sub_num) +  
##     (1 | target_category)
##    Data: trial_corrected_accuracy
## 
## REML criterion at convergence: 2248.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.2103 -0.6176 -0.0250  0.6570  2.8127 
## 
## Random effects:
##  Groups          Name                    Variance  Std.Dev. Corr       
##  sub_num         (Intercept)             0.0028677 0.05355             
##                  target_typicality_z     0.0033167 0.05759   0.27      
##                  distractor_typicality_z 0.0033408 0.05780  -0.14 -0.99
##  target_category (Intercept)             0.0002616 0.01617             
##  Residual                                0.1175638 0.34288             
## Number of obs: 3088, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                          Estimate Std. Error        df t value Pr(>|t|)   
## (Intercept)              0.073290   0.011762  5.201755   6.231  0.00135 **
## target_typicality_z      0.006952   0.014313 97.926779   0.486  0.62828   
## distractor_typicality_z  0.005153   0.014234 91.456627   0.362  0.71817   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) trgt__
## trgt_typcl_  0.066       
## dstrctr_ty_ -0.037 -0.894
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')

confint(m_5_1_1,method="Wald")

##                             2.5 %     97.5 %
## .sig01                         NA         NA
## .sig02                         NA         NA
## .sigma                         NA         NA
## (Intercept)          0.0498745657 0.09620693
## target_typicality_z -0.0006958822 0.02421020

5.2. Category and Item-level analysis

Next, we investigate category- (target word) and item-level (target image) variation in proportion target looking.

Summarize overall target looking

Target Word

# summarize average accuracy within participant (by word alone)
avg_corrected_target_looking_by_word <- trial_corrected_accuracy  %>%
  group_by(sub_num, target_category) %>%
  summarize(N=n(),
            mean_age = mean(age),
            mean_age_mo = mean(age_mo),
            average_corrected_target_looking=mean(corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=average_corrected_target_looking-ci,
            upper_ci=average_corrected_target_looking+ci,
            average_critical_window_looking=mean(mean_target_looking_critical,na.rm=TRUE),
            critical_window_ci = qt(0.975, N-1)*sd(mean_target_looking_critical,na.rm=T)/sqrt(N),
            critical_window_lower_ci=average_critical_window_looking-critical_window_ci,
            critical_window_upper_ci=average_critical_window_looking+critical_window_ci,
            average_baseline_window_looking=mean(mean_target_looking_baseline,na.rm=TRUE),
            baseline_window_ci = qt(0.975, N-1)*sd(mean_target_looking_baseline,na.rm=T)/sqrt(N),
            baseline_window_lower_ci=average_baseline_window_looking-baseline_window_ci,
            baseline_window_upper_ci=average_baseline_window_looking+baseline_window_ci)

# summarize average accuracy within participant (by word split by typicality)
avg_corrected_target_looking_by_typicality_word <- trial_corrected_accuracy  %>%
  group_by(sub_num, condition,target_category) %>%
  summarize(N=n(),
            mean_age = mean(age),
            mean_age_mo = mean(age_mo),
            average_corrected_target_looking=mean(corrected_target_looking,na.rm=TRUE),
            average_critical_window_looking=mean(mean_target_looking_critical,na.rm=TRUE),
            average_baseline_window_looking=mean(mean_target_looking_baseline,na.rm=TRUE))

#overall summarized looking
#by word alone
overall_target_looking_by_word <- avg_corrected_target_looking_by_word %>%
  group_by(target_category) %>%
  summarize(N=n(),
            corrected_target_looking=mean(average_corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(average_corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=corrected_target_looking-ci,
            upper_ci=corrected_target_looking+ci,
            target_looking_critical_window=mean(average_critical_window_looking,na.rm=TRUE),
            ci_critical_window=qt(0.975, N-1)*sd(average_critical_window_looking,na.rm=T)/sqrt(N),
            lower_ci_critical_window=target_looking_critical_window-ci_critical_window,
            upper_ci_critical_window=target_looking_critical_window+ci_critical_window,
            target_looking_baseline_window=mean(average_baseline_window_looking,na.rm=TRUE),
            ci_baseline_window=qt(0.975, N-1)*sd(average_baseline_window_looking,na.rm=T)/sqrt(N),
            lower_ci_baseline_window=target_looking_baseline_window-ci_baseline_window,
            upper_ci_baseline_window=target_looking_baseline_window+ci_baseline_window
            )
#by word split by typicality
overall_target_looking_by_typicality_word <- avg_corrected_target_looking_by_typicality_word %>%
  group_by(condition,target_category) %>%
  summarize(N=n(),
            corrected_target_looking=mean(average_corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(average_corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=corrected_target_looking-ci,
            upper_ci=corrected_target_looking+ci,
            target_looking_critical_window=mean(average_critical_window_looking,na.rm=TRUE),
            ci_critical_window=qt(0.975, N-1)*sd(average_critical_window_looking,na.rm=T)/sqrt(N),
            lower_ci_critical_window=target_looking_critical_window-ci_critical_window,
            upper_ci_critical_window=target_looking_critical_window+ci_critical_window,
            target_looking_baseline_window=mean(average_baseline_window_looking,na.rm=TRUE),
            ci_baseline_window=qt(0.975, N-1)*sd(average_baseline_window_looking,na.rm=T)/sqrt(N),
            lower_ci_baseline_window=target_looking_baseline_window-ci_baseline_window,
            upper_ci_baseline_window=target_looking_baseline_window+ci_baseline_window
            )

Overall, participants showed robust learning of all four words, in both typicality conditions.

overall_target_looking_by_word %>%
  select(target_category:upper_ci) %>%
  knitr::kable()

target_category	N	corrected_target_looking	ci	lower_ci	upper_ci
bird	84	0.0828352	0.0289568	0.0538784	0.1117921
cat	84	0.0846898	0.0274928	0.0571970	0.1121825
dog	84	0.0452197	0.0253637	0.0198560	0.0705835
fish	84	0.0645363	0.0307689	0.0337674	0.0953052

overall_target_looking_by_typicality_word %>%
  select(target_category:upper_ci) %>%
  knitr::kable()

condition	target_category	N	corrected_target_looking	ci	lower_ci	upper_ci
atypical	bird	84	0.0952772	0.0412225	0.0540548	0.1364997
atypical	cat	84	0.0721099	0.0385986	0.0335113	0.1107084
atypical	dog	84	0.0237760	0.0393909	-0.0156149	0.0631669
atypical	fish	84	0.0681816	0.0426735	0.0255081	0.1108551
typical	bird	84	0.0728658	0.0360956	0.0367702	0.1089614
typical	cat	84	0.1039214	0.0386892	0.0652323	0.1426106
typical	dog	84	0.0710628	0.0354239	0.0356389	0.1064867
typical	fish	84	0.0597611	0.0415034	0.0182577	0.1012645

#checking the typicality effect for bird
t.test(
  filter(avg_corrected_target_looking_by_typicality_word,condition=="typical"&target_category=="bird")$average_corrected_target_looking,
  filter(avg_corrected_target_looking_by_typicality_word,condition=="atypical"&target_category=="bird")$average_corrected_target_looking,
  paired=TRUE
)

## 
##  Paired t-test
## 
## data:  filter(avg_corrected_target_looking_by_typicality_word, condition == "typical" & target_category == "bird")$average_corrected_target_looking and filter(avg_corrected_target_looking_by_typicality_word, condition == "atypical" & target_category == "bird")$average_corrected_target_looking
## t = -0.91048, df = 83, p-value = 0.3652
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -0.07136948  0.02654664
## sample estimates:
## mean difference 
##     -0.02241142

#checking the typicality effect for bird
t.test(
  filter(avg_corrected_target_looking_by_typicality_word,condition=="typical"&target_category=="cat")$average_corrected_target_looking,
  filter(avg_corrected_target_looking_by_typicality_word,condition=="atypical"&target_category=="cat")$average_corrected_target_looking,
  paired=TRUE
)

## 
##  Paired t-test
## 
## data:  filter(avg_corrected_target_looking_by_typicality_word, condition == "typical" & target_category == "cat")$average_corrected_target_looking and filter(avg_corrected_target_looking_by_typicality_word, condition == "atypical" & target_category == "cat")$average_corrected_target_looking
## t = 1.2173, df = 83, p-value = 0.2269
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -0.02016634  0.08378945
## sample estimates:
## mean difference 
##      0.03181156

#checking the typicality effect for dog
t.test(
  filter(avg_corrected_target_looking_by_typicality_word,condition=="typical"&target_category=="dog")$average_corrected_target_looking,
  filter(avg_corrected_target_looking_by_typicality_word,condition=="atypical"&target_category=="dog")$average_corrected_target_looking,
  paired=TRUE
)

## 
##  Paired t-test
## 
## data:  filter(avg_corrected_target_looking_by_typicality_word, condition == "typical" & target_category == "dog")$average_corrected_target_looking and filter(avg_corrected_target_looking_by_typicality_word, condition == "atypical" & target_category == "dog")$average_corrected_target_looking
## t = 1.7506, df = 83, p-value = 0.08371
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -0.006439375  0.101012983
## sample estimates:
## mean difference 
##       0.0472868

#checking the typicality effect for fish
t.test(
  filter(avg_corrected_target_looking_by_typicality_word,condition=="typical"&target_category=="fish")$average_corrected_target_looking,
  filter(avg_corrected_target_looking_by_typicality_word,condition=="atypical"&target_category=="fish")$average_corrected_target_looking,
  paired=TRUE
)

## 
##  Paired t-test
## 
## data:  filter(avg_corrected_target_looking_by_typicality_word, condition == "typical" & target_category == "fish")$average_corrected_target_looking and filter(avg_corrected_target_looking_by_typicality_word, condition == "atypical" & target_category == "fish")$average_corrected_target_looking
## t = -0.28603, df = 83, p-value = 0.7756
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -0.06697470  0.05013365
## sample estimates:
## mean difference 
##    -0.008420526

Plot

pal <- wes_palette("Rushmore1", n=5)
set.seed(1)
jitterer <- position_jitter(width = .05,seed=1)
p3 <- ggplot(avg_corrected_target_looking_by_typicality_word,aes(x=condition,y=average_corrected_target_looking, fill=condition))+
  geom_half_violin(data=filter(avg_corrected_target_looking_by_typicality_word, condition=="atypical"),position = position_nudge(x = -.1, y = 0), width=1,trim = FALSE, alpha = .8,color=NA,side="l")+
  geom_half_violin(data=filter(avg_corrected_target_looking_by_typicality_word, condition=="typical"),position = position_nudge(x = .1, y = 0), width=1,trim = FALSE, alpha = .8,color=NA,side="r")+
  geom_path(aes(group=sub_num),color="black",fill=NA,alpha=0.05,size=0.75,position=jitterer)+
  geom_point(aes(color=condition,group=sub_num), size = 2.5, alpha=0.05,position=jitterer)+
  geom_point(data=overall_target_looking_by_typicality_word,aes(y=corrected_target_looking),color="black",size=1.8)+
  geom_line(data=overall_target_looking_by_typicality_word,aes(y=corrected_target_looking,group=1),color="black",size=1.5)+
  geom_errorbar(data=overall_target_looking_by_typicality_word,aes(y=corrected_target_looking,ymin=lower_ci,ymax=upper_ci),width=0,color="black")+
  #geom_boxplot(outlier.shape = NA, alpha = .5, width = .1, colour = "black")+
  #scale_colour_brewer(palette = "Dark2")+
  #scale_fill_brewer(palette = "Dark2")+
  geom_hline(yintercept=0,linetype="dashed")+
  scale_colour_manual(values=pal[c(3,4)])+
  scale_fill_manual(values=pal[c(3,4)])+
  facet_wrap(.~target_category)+
  theme(legend.position="none")+
  xlab("Typicality Condition")+
  ylab("Baseline-Corrected\nProportion Target Looking")+
  theme(axis.title.x = element_text(face="bold", size=20),
        axis.text.x  = element_text(size=16),
        axis.title.y = element_text(face="bold", size=20),
        axis.text.y  = element_text(size=16),
        strip.text.x = element_text(size = 16,face="bold"))


ggsave(here::here("..","figures","baseline_corrected_accuracy_by_category.png"),width=7,height=6)

Target Image

# summarize average accuracy within participant
avg_corrected_target_looking_by_image <- trial_corrected_accuracy  %>%
  group_by(sub_num, condition,target_category,target_image,target_typicality_z) %>%
  summarize(N=n(),
            mean_age = mean(age),
            mean_age_mo = mean(age_mo),
            average_corrected_target_looking=mean(corrected_target_looking,na.rm=TRUE),
            average_critical_window_looking=mean(mean_target_looking_critical,na.rm=TRUE),
            average_baseline_window_looking=mean(mean_target_looking_baseline,na.rm=TRUE))

#baseline-corrected target looking summarized overall
overall_target_looking_by_image <- avg_corrected_target_looking_by_image %>%
  group_by(condition,target_category,target_image,target_typicality_z) %>%
  summarize(N=n(),
            corrected_target_looking=mean(average_corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(average_corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=corrected_target_looking-ci,
            upper_ci=corrected_target_looking+ci,
            target_looking_critical_window=mean(average_critical_window_looking,na.rm=TRUE),
            ci_critical_window=qt(0.975, N-1)*sd(average_critical_window_looking,na.rm=T)/sqrt(N),
            lower_ci_critical_window=target_looking_critical_window-ci_critical_window,
            upper_ci_critical_window=target_looking_critical_window+ci_critical_window,
            target_looking_baseline_window=mean(average_baseline_window_looking,na.rm=TRUE),
            ci_baseline_window=qt(0.975, N-1)*sd(average_baseline_window_looking,na.rm=T)/sqrt(N),
            lower_ci_baseline_window=target_looking_baseline_window-ci_baseline_window,
            upper_ci_baseline_window=target_looking_baseline_window+ci_baseline_window
            ) %>%
  rename(target_image_name=target_image) %>%
  mutate(target_image=str_replace(target_image_name,"_600x600",""),
         target_image_path=here("images",paste(target_image_name,".png",sep="")))
overall_target_looking_by_image %>%
  ungroup() %>%
  relocate(target_image) %>%
  select(-target_image_path,-target_image_name) %>%
  knitr::kable()

target_image	condition	target_category	target_typicality_z	N	corrected_target_looking	ci	lower_ci	upper_ci	target_looking_critical_window	ci_critical_window	lower_ci_critical_window	upper_ci_critical_window	target_looking_baseline_window	ci_baseline_window	lower_ci_baseline_window	upper_ci_baseline_window
heron	atypical	bird	-0.2912701	82	0.1408195	0.0662388	0.0745807	0.2070583	0.5547662	0.0555783	0.4991879	0.6103445	0.4139467	0.0401921	0.3737546	0.4541388
kingfisher	atypical	bird	-0.1281589	79	0.0382778	0.0710872	-0.0328093	0.1093650	0.4856289	0.0624170	0.4232120	0.5480459	0.4473511	0.0419578	0.4053933	0.4893090
kookaburra	atypical	bird	-1.0835249	78	0.1066172	0.0567018	0.0499154	0.1633190	0.5541817	0.0470623	0.5071194	0.6012440	0.4475645	0.0412278	0.4063367	0.4887924
cornishrex	atypical	cat	-1.1767313	80	0.0763216	0.0675627	0.0087589	0.1438843	0.5409182	0.0587443	0.4821739	0.5996625	0.4645966	0.0395096	0.4250871	0.5041062
oriental	atypical	cat	-1.1301281	80	0.1527616	0.0690103	0.0837513	0.2217719	0.6565296	0.0531853	0.6033443	0.7097148	0.5037680	0.0468078	0.4569601	0.5505758
sphynx	atypical	cat	-1.8058748	83	0.0003310	0.0680594	-0.0677284	0.0683904	0.6153968	0.0496319	0.5657649	0.6650288	0.6150658	0.0433231	0.5717427	0.6583890
afghanhound	atypical	dog	-1.0136201	79	0.0621100	0.0636254	-0.0015154	0.1257354	0.6036402	0.0522234	0.5514168	0.6558636	0.5415302	0.0419835	0.4995466	0.5835137
bassethound	atypical	dog	-0.5708895	81	0.0432086	0.0742969	-0.0310883	0.1175054	0.6520520	0.0542444	0.5978076	0.7062964	0.6088435	0.0478269	0.5610165	0.6566704
sheepdog	atypical	dog	-1.4563507	82	-0.0268143	0.0617432	-0.0885574	0.0349289	0.4743607	0.0503071	0.4240536	0.5246678	0.5011750	0.0415525	0.4596225	0.5427275
betafish	atypical	fish	-0.5475879	83	0.0882696	0.0645190	0.0237506	0.1527886	0.5323232	0.0579734	0.4743497	0.5902966	0.4440536	0.0394941	0.4045594	0.4835477
lionfish	atypical	fish	-0.9670168	80	0.0029581	0.0692744	-0.0663163	0.0722325	0.5203641	0.0572911	0.4630731	0.5776552	0.5174060	0.0401878	0.4772183	0.5575938
sturgeon	atypical	fish	-0.7573023	81	0.1372774	0.0735684	0.0637090	0.2108458	0.4896405	0.0612244	0.4284161	0.5508649	0.3523631	0.0476130	0.3047501	0.3999761
cardinal	typical	bird	0.6873975	83	0.0761337	0.0577969	0.0183368	0.1339306	0.5527972	0.0460688	0.5067284	0.5988660	0.4766635	0.0415477	0.4351158	0.5182111
robin	typical	bird	0.7340007	82	0.1123138	0.0706687	0.0416452	0.1829825	0.5664190	0.0527234	0.5136956	0.6191424	0.4541051	0.0422689	0.4118363	0.4963740
sparrow	typical	bird	1.0369217	83	0.0294041	0.0489869	-0.0195828	0.0783909	0.5079121	0.0431239	0.4647882	0.5510359	0.4785080	0.0381717	0.4403363	0.5166796
arabianmau	typical	cat	0.8272072	82	0.0719848	0.0501193	0.0218655	0.1221041	0.5958545	0.0504340	0.5454205	0.6462885	0.5238697	0.0351796	0.4886901	0.5590493
chartreux	typical	cat	0.6407943	81	0.1536233	0.0723942	0.0812291	0.2260175	0.5942010	0.0568159	0.5373850	0.6510169	0.4405777	0.0513137	0.3892640	0.4918914
tabby	typical	cat	1.3631442	82	0.0860622	0.0732891	0.0127732	0.1593513	0.6226850	0.0616445	0.5610405	0.6843294	0.5366227	0.0420258	0.4945969	0.5786485
beagle	typical	dog	1.1534297	79	0.1038370	0.0651526	0.0386844	0.1689896	0.6290305	0.0515945	0.5774359	0.6806250	0.5251935	0.0392946	0.4858989	0.5644881
germanshepherd	typical	dog	1.1767313	81	0.0822380	0.0647282	0.0175098	0.1469662	0.5672133	0.0478993	0.5193139	0.6151126	0.4849753	0.0410271	0.4439483	0.5260024
goldenretriever	typical	dog	0.9670168	83	0.0259201	0.0582506	-0.0323305	0.0841707	0.5466143	0.0462486	0.5003657	0.5928629	0.5206942	0.0420201	0.4786741	0.5627143
bass	typical	fish	0.7806040	81	0.0633932	0.0683873	-0.0049941	0.1317805	0.5240357	0.0597066	0.4643291	0.5837422	0.4606424	0.0378064	0.4228361	0.4984488
bluegill	typical	fish	0.8039056	81	0.0721545	0.0641440	0.0080105	0.1362984	0.5666383	0.0535123	0.5131260	0.6201506	0.4944838	0.0430493	0.4514345	0.5375332
clownfish	typical	fish	0.7573023	80	0.0423539	0.0621051	-0.0197512	0.1044590	0.5335050	0.0493777	0.4841273	0.5828827	0.4911511	0.0449664	0.4461847	0.5361175

Plot

ggplot(overall_target_looking_by_image,aes(reorder(target_image,corrected_target_looking),corrected_target_looking))+
  geom_image(aes(y=corrected_target_looking+0.1,image=target_image_path),size=.1)+
  geom_hline(yintercept=0,linetype="dashed")+
  geom_errorbar(aes(ymin=lower_ci,ymax=upper_ci,color=condition),width=0)+
  geom_point(aes(color=condition),size=3)+
  xlab("Target Image")+
  ylab("Baseline-Corrected\nProportion Target Looking")+
  theme(axis.title.x = element_text(face="bold", size=20),
        axis.text.x  = element_text(size=16,angle=90,vjust=0.5),
        axis.title.y = element_text(face="bold", size=20),
        axis.text.y  = element_text(size=16),
        strip.text.x = element_text(size = 16,face="bold"),
        legend.position=c(0.8,0.15)
        )+
  scale_color_manual(values=pal[c(3,4)])

ggsave(here::here("..","figures","baseline_corrected_accuracy_by_word.png"),width=9,height=6)

5.3. Reliability

5.3.1. How correlated is accuracy within participants between session 1 and session 2

avg_corrected_target_looking_by_session_wide <- avg_corrected_target_looking_by_session %>%
  ungroup() %>%
  select(sub_num,session,average_corrected_target_looking) %>%
  pivot_wider(names_from=session,names_prefix="session_",values_from=average_corrected_target_looking)

#compute correlation
cor.test(
  avg_corrected_target_looking_by_session_wide$session_1,
  avg_corrected_target_looking_by_session_wide$session_2)

## 
##  Pearson's product-moment correlation
## 
## data:  avg_corrected_target_looking_by_session_wide$session_1 and avg_corrected_target_looking_by_session_wide$session_2
## t = 2.4924, df = 78, p-value = 0.01481
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.05518076 0.46365258
## sample estimates:
##       cor 
## 0.2716047

ggplot(avg_corrected_target_looking_by_session_wide,aes(session_1,session_2)) +
  geom_point()+
  geom_smooth(method="lm")+
  annotate("text",label="r=.27, t(78)=2.49, p=.01",x=-0.3,y=0.25,size=5)+
  xlab("Session 1\nAverage Baseline-Corrected Proportion Target Looking")+
  ylab("Session 2\nAverage Baseline-Corrected Proportion Target Looking")

ggsave(here::here("..","figures","session_correlation.png"),width=9,height=6)

avg_corrected_target_looking_by_typicality_session_wide <- avg_corrected_target_looking_by_typicality_session %>%
  ungroup() %>%
  select(sub_num,session,condition,average_corrected_target_looking) %>%
  pivot_wider(names_from=session,names_prefix="session_",values_from=average_corrected_target_looking)

#compute correlation
#typical
cor.test(
  filter(avg_corrected_target_looking_by_typicality_session_wide,condition=="typical")$session_1,
  filter(avg_corrected_target_looking_by_typicality_session_wide,condition=="typical")$session_2)

## 
##  Pearson's product-moment correlation
## 
## data:  filter(avg_corrected_target_looking_by_typicality_session_wide, condition == "typical")$session_1 and filter(avg_corrected_target_looking_by_typicality_session_wide, condition == "typical")$session_2
## t = 1.3137, df = 77, p-value = 0.1928
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.07552129  0.35746912
## sample estimates:
##       cor 
## 0.1480615

#atypical
cor.test(
  filter(avg_corrected_target_looking_by_typicality_session_wide,condition=="atypical")$session_1,
  filter(avg_corrected_target_looking_by_typicality_session_wide,condition=="atypical")$session_2)

## 
##  Pearson's product-moment correlation
## 
## data:  filter(avg_corrected_target_looking_by_typicality_session_wide, condition == "atypical")$session_1 and filter(avg_corrected_target_looking_by_typicality_session_wide, condition == "atypical")$session_2
## t = 1.421, df = 78, p-value = 0.1593
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.06306279  0.36580436
## sample estimates:
##       cor 
## 0.1588552

ggplot(avg_corrected_target_looking_by_typicality_session_wide,aes(session_1,session_2,color=condition)) +
  geom_point()+
  geom_smooth(method="lm")+
  xlab("Session 1\nAverage Baseline-Corrected Proportion Target Looking")+
  ylab("Session 2\nAverage Baseline-Corrected Proportion Target Looking")+
  facet_wrap(~condition)+
  scale_color_manual(values=pal[c(3,4)])+
  theme(legend.position="none")

ggsave(here::here("..","figures","session_correlation_by_typicality.png"),width=9,height=6)

5.3.2. ICCs

df_for_icc <- trial_corrected_accuracy %>%
  #some light renaming to use Peekbank icc function
  mutate(
    administration_id = sub_num
  ) %>%
  unite("trial_id", administration_id, trial_number,remove=F) %>%
  mutate(
    target_label=target_image
  )

#ICC for participants
icc_participants <- df_for_icc %>%
  get_icc(object = "administration",column="corrected_target_looking",type_icc="consistency")
icc_participants_baseline <- df_for_icc %>%
  get_icc(object = "administration",column="mean_target_looking_baseline",type_icc="consistency")
icc_participants_critical <- df_for_icc %>%
  get_icc(object = "administration",column="mean_target_looking_critical",type_icc="consistency")


#ICC for stimuli
icc_stimuli <- df_for_icc %>%
  get_icc(object = "stimulus",column="corrected_target_looking",type_icc="consistency")
icc_stimuli_baseline <- df_for_icc %>%
  get_icc(object = "stimulus",column="mean_target_looking_baseline",type_icc="consistency")
icc_stimuli_critical <-  df_for_icc %>%
  get_icc(object = "stimulus",column="mean_target_looking_critical",type_icc="consistency")

5.4. Exploring alternative trial-based inclusion criteria

Participants were required to contribute at least 24 valid trials in order to be included in the final sample. Here, we explore the impact of this criterion on whether we observe a typicality effect, by estimating the typicality effect for a range of looser and stricter trial-based exclusion criteria

min_trials_required_list = c(4,8,12,16,20,24,28,32,36,40,44,48)

# set up summarized dataset to use
subj_typ_data <- trial_corrected_accuracy_all %>%
  #apply exclusion criteria to trials
  filter(exclude_frame_rate==0) %>%
  filter(exclude_technical_issue==0) %>%
  filter(useable_window==1) %>%
  filter(age_exclusion==0) %>%
  group_by(sub_num,condition) %>%
  summarize(
    N=n(),
    average_corrected_target_looking=mean(corrected_target_looking,na.rm=TRUE)
    ) %>%
  ungroup() %>%
  group_by(sub_num) %>%
  mutate(total_trials=sum(N,na.rm=TRUE)) %>%
  pivot_wider(names_from=condition,values_from=c(N,average_corrected_target_looking)) %>%
  ungroup() 

#add and apply min trial exclusion criteria,
#creating nested dataframes for each minimum trial exclusion criterion
#then test the typicality effect within each dataset and store the results

typ_effect_min_valid_trials <- expand_grid(
  subj_typ_data,
  min_valid_trials_req = min_trials_required_list
) %>%
  #apply min trial exclusion criterion 
  group_by(min_valid_trials_req) %>%
  filter(total_trials>=min_valid_trials_req) %>%
  mutate(
    N=length(sub_num)
  ) %>%
  group_by(min_valid_trials_req,N) %>%
  #nest the data
  nest() %>%
  mutate(t_test = map(data, ~ t.test(.x$average_corrected_target_looking_typical, .x$average_corrected_target_looking_atypical,paired = T)),
         result = map(t_test, tidy)
         ) %>%
  unnest(result)

# typ_effect_min_valid_trials %>%
#   knitr::kable()

## plot the result
ggplot(typ_effect_min_valid_trials, aes(min_valid_trials_req,estimate))+
  geom_errorbar(aes(ymin=conf.low,ymax=conf.high),width=0)+
  geom_point(size=3)+
  geom_hline(yintercept=0,linetype="dashed")+
  geom_text(aes(label=N),nudge_y = 0.07)+
  ylab("Estimated Participant-Level Typicality Effect")+
  xlab("Minimum Number of Trials Required for Inclusion")

ggsave(here::here("..","figures","typicality_effect_min_trials_for_inclusion.png"),width=9,height=6)

5.5. Testing the main results with a final sample of N=80

In our Stage 1 manuscript, we preregistered a sample of N=80. Our current results report data from all participants who contributed valid data, leading to a final N of 84 participants. Here, we remove the data from the final 4 participants who contributed data on Lookit and re-run the main analyses from Aim 1 (1.1 and 1.2), to ensure that the decision to include all participants did not change the outcome of the study.

Remove the final 4 participants

CAT_343, CAT_344, CAT_345, and CAT_346 were the final 4 participants contributing data on Lookit.

subj_to_remove <- c("CAT_343","CAT_344","CAT_345","CAT_346")
trial_corrected_accuracy_red <- trial_corrected_accuracy_all %>%
  filter(exclude_participant==0) %>%
  filter(trial_exclusion==0) %>%
  filter(!(sub_num %in% subj_to_remove))

# summarize by-participant and typicality
avg_corrected_target_looking_by_typicality_red <- trial_corrected_accuracy_red  %>%
  group_by(sub_num, condition) %>%
  summarize(N=n(),
            mean_age = mean(age),
            mean_age_mo = mean(age_mo),
            average_corrected_target_looking=mean(corrected_target_looking,na.rm=TRUE),
            se=sd(corrected_target_looking,na.rm=T)/sqrt(N),
            ci=qt(0.975, N-1)*sd(corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=average_corrected_target_looking-ci,
            upper_ci=average_corrected_target_looking+ci,
            lower_se=average_corrected_target_looking-se,
            upper_se=average_corrected_target_looking+se)

#baseline-corrected target looking summarized overall
overall_corrected_target_looking_by_typicality_red <- avg_corrected_target_looking_by_typicality_red %>%
  group_by(condition) %>%
  summarize(N=n(),
            corrected_target_looking=mean(average_corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(average_corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=corrected_target_looking-ci,
            upper_ci=corrected_target_looking+ci)

overall_corrected_target_looking_by_typicality_red %>%
  knitr::kable()

condition	N	corrected_target_looking	ci	lower_ci	upper_ci
atypical	80	0.0605700	0.0194323	0.0411377	0.0800024
typical	80	0.0766292	0.0216437	0.0549855	0.0982729

Participant-level analysis

avg_corrected_target_looking_by_typicality_red <- avg_corrected_target_looking_by_typicality_red %>%
  mutate(
    typicality_condition_c = case_when(
      condition == "atypical" ~ -0.5,
      condition == "typical" ~ 0.5,
      TRUE ~ NA_real_
    ),
    typicality_condition_typ = case_when(
      condition == "atypical" ~ -1,
      condition == "typical" ~ 0,
      TRUE ~ NA_real_
    ),
    typicality_condition_atyp = case_when(
      condition == "atypical" ~ 0,
      condition == "typical" ~ 1,
      TRUE ~ NA_real_
    ),
  )

m_1_1_red <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_c + (1+ typicality_condition_c|sub_num),data=avg_corrected_target_looking_by_typicality_red,control=lmerControl(check.nobs.vs.nlev= "ignore",check.nobs.vs.nRE= "ignore"))
summary(m_1_1_red)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_corrected_target_looking ~ 1 + typicality_condition_c +  
##     (1 + typicality_condition_c | sub_num)
##    Data: avg_corrected_target_looking_by_typicality_red
## Control: 
## lmerControl(check.nobs.vs.nlev = "ignore", check.nobs.vs.nRE = "ignore")
## 
## REML criterion at convergence: -301.6
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.16425 -0.36910  0.07516  0.41158  1.85866 
## 
## Random effects:
##  Groups   Name                   Variance Std.Dev. Corr
##  sub_num  (Intercept)            0.003331 0.05771      
##           typicality_condition_c 0.004636 0.06809  0.23
##  Residual                        0.004052 0.06366      
## Number of obs: 160, groups:  sub_num, 80
## 
## Fixed effects:
##                         Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)             0.068600   0.008183 79.000504   8.383 1.56e-12 ***
## typicality_condition_c  0.016059   0.012620 78.999366   1.273    0.207    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.111

confint(m_1_1_red,method="Wald")

##                               2.5 %     97.5 %
## .sig01                           NA         NA
## .sig02                           NA         NA
## .sig03                           NA         NA
## .sigma                           NA         NA
## (Intercept)             0.052561283 0.08463797
## typicality_condition_c -0.008674928 0.04079339

There remained no significant effect of typicality in the participant-level analysis.

## Typical word recognition
# recentering the model on the typical condition to make the intercept interpretable
m_1_1_3_typ_red <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_typ + (1+ typicality_condition_typ|sub_num),data=avg_corrected_target_looking_by_typicality_red,control=lmerControl(check.nobs.vs.nlev= "ignore",check.nobs.vs.nRE= "ignore"))
summary(m_1_1_3_typ_red)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_corrected_target_looking ~ 1 + typicality_condition_typ +  
##     (1 + typicality_condition_typ | sub_num)
##    Data: avg_corrected_target_looking_by_typicality_red
## Control: 
## lmerControl(check.nobs.vs.nlev = "ignore", check.nobs.vs.nRE = "ignore")
## 
## REML criterion at convergence: -301.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.3642 -0.4032  0.0821  0.4496  2.0304 
## 
## Random effects:
##  Groups   Name                     Variance Std.Dev. Corr
##  sub_num  (Intercept)              0.004623 0.06799      
##           typicality_condition_typ 0.003069 0.05540  0.65
##  Residual                          0.004836 0.06954      
## Number of obs: 160, groups:  sub_num, 80
## 
## Fixed effects:
##                          Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)               0.07663    0.01087 78.99978   7.047 6.07e-10 ***
## typicality_condition_typ  0.01606    0.01262 79.00009   1.273    0.207    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.664 
## optimizer (nloptwrap) convergence code: 0 (OK)
## unable to evaluate scaled gradient
## Model failed to converge: degenerate  Hessian with 1 negative eigenvalues

confint(m_1_1_3_typ_red,method="Wald")

##                                 2.5 %     97.5 %
## .sig01                             NA         NA
## .sig02                             NA         NA
## .sig03                             NA         NA
## .sigma                             NA         NA
## (Intercept)               0.055317025 0.09794146
## typicality_condition_typ -0.008674805 0.04079327

#effect size
cohens_d(avg_corrected_target_looking_by_typicality_red$average_corrected_target_looking[avg_corrected_target_looking_by_typicality_red$condition=="typical"])

## Cohen's d |       95% CI
## ------------------------
## 0.79      | [0.53, 1.04]

## Atypical word recognition
# recentering the model on the atypical condition to make the intercept interpretable
m_1_1_3_atyp_red <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_atyp + (1+ typicality_condition_atyp|sub_num),data=avg_corrected_target_looking_by_typicality_red,control=lmerControl(check.nobs.vs.nlev= "ignore",check.nobs.vs.nRE= "ignore"))
summary(m_1_1_3_atyp_red)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_corrected_target_looking ~ 1 + typicality_condition_atyp +  
##     (1 + typicality_condition_atyp | sub_num)
##    Data: avg_corrected_target_looking_by_typicality_red
## Control: 
## lmerControl(check.nobs.vs.nlev = "ignore", check.nobs.vs.nRE = "ignore")
## 
## REML criterion at convergence: -301.6
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.26462 -0.38622  0.07864  0.43066  1.94491 
## 
## Random effects:
##  Groups   Name                      Variance Std.Dev. Corr 
##  sub_num  (Intercept)               0.003188 0.05646       
##           typicality_condition_atyp 0.003866 0.06218  -0.29
##  Residual                           0.004437 0.06661       
## Number of obs: 160, groups:  sub_num, 80
## 
## Fixed effects:
##                            Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)                0.060570   0.009763 78.999551   6.204 2.37e-08 ***
## typicality_condition_atyp  0.016059   0.012620 78.999798   1.273    0.207    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ -0.553
## optimizer (nloptwrap) convergence code: 0 (OK)
## unable to evaluate scaled gradient
## Model failed to converge: degenerate  Hessian with 1 negative eigenvalues

confint(m_1_1_3_atyp_red,method="Wald")

##                                  2.5 %     97.5 %
## .sig01                              NA         NA
## .sig02                              NA         NA
## .sig03                              NA         NA
## .sigma                              NA         NA
## (Intercept)                0.041435242 0.07970478
## typicality_condition_atyp -0.008674823 0.04079328

#effect size
cohens_d(avg_corrected_target_looking_by_typicality_red$average_corrected_target_looking[avg_corrected_target_looking_by_typicality_red$condition=="atypical"])

## Cohen's d |       95% CI
## ------------------------
## 0.69      | [0.45, 0.94]

Infants recognized both typical and atypical exemplars, with similar effect sizes.

Trial-level analysis

trial_corrected_accuracy_red <- trial_corrected_accuracy_red %>%
  mutate(
    typicality_condition_c = case_when(
      condition == "atypical" ~ -0.5,
      condition == "typical" ~ 0.5,
      TRUE ~ NA_real_
    ),
    typicality_condition_typ = case_when(
      condition == "atypical" ~ -1,
      condition == "typical" ~ 0,
      TRUE ~ NA_real_
    ),
    typicality_condition_atyp = case_when(
      condition == "atypical" ~ 0,
      condition == "typical" ~ 1,
      TRUE ~ NA_real_
    ),
  )

#model with typicality random intercept has singular fit but yields basically identical results
m_1_2_red <- lmer(corrected_target_looking ~ 1 + typicality_condition_c + 
            (1 | sub_num) +
            (1|target_category),
          data=trial_corrected_accuracy_red)
summary(m_1_2_red)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking ~ 1 + typicality_condition_c + (1 |  
##     sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy_red
## 
## REML criterion at convergence: 2150.3
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -3.13603 -0.61726 -0.03279  0.66064  2.75427 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0022297 0.04722 
##  target_category (Intercept) 0.0001792 0.01339 
##  Residual                    0.1197725 0.34608 
## Number of obs: 2926, groups:  sub_num, 80; target_category, 4
## 
## Fixed effects:
##                         Estimate Std. Error        df t value Pr(>|t|)   
## (Intercept)            6.963e-02  1.069e-02 5.172e+00   6.514  0.00112 **
## typicality_condition_c 1.275e-02  1.281e-02 2.859e+03   0.996  0.31955   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ -0.001

confint(m_1_2_red,method="Wald")

##                              2.5 %     97.5 %
## .sig01                          NA         NA
## .sig02                          NA         NA
## .sigma                          NA         NA
## (Intercept)             0.04867897 0.09057927
## typicality_condition_c -0.01235235 0.03785493

The trial-level model also yields no significant typicality effect.

Session Info

sessionInfo()

## R version 4.2.2 (2022-10-31)
## Platform: aarch64-apple-darwin20 (64-bit)
## Running under: macOS 14.2.1
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.2-arm64/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.2-arm64/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] patchwork_1.1.2       agreement_0.0.0.9003  broom_1.0.4          
##  [4] sessioninfo_1.2.2     ggimage_0.3.3         effectsize_0.8.6     
##  [7] papaja_0.1.1          tinylabels_0.2.3      broom.mixed_0.2.9.4  
## [10] JWileymisc_1.4.1      multilevelTools_0.1.1 car_3.1-1            
## [13] carData_3.0-5         gghalves_0.1.4        wesanderson_0.3.6    
## [16] TOSTER_0.7.1          lmerTest_3.1-3        lme4_1.1-31          
## [19] Matrix_1.5-1          readxl_1.4.3          here_1.0.1           
## [22] cowplot_1.1.1         janitor_2.2.0         lubridate_1.9.3      
## [25] forcats_1.0.0         stringr_1.5.0         dplyr_1.1.2          
## [28] purrr_1.0.1           readr_2.1.4           tidyr_1.3.0          
## [31] tibble_3.2.1          ggplot2_3.4.4         tidyverse_2.0.0      
## 
## loaded via a namespace (and not attached):
##   [1] utf8_1.2.2           rms_6.7-1            tidyselect_1.2.0    
##   [4] htmlwidgets_1.6.1    grid_4.2.2           munsell_0.5.0       
##   [7] ragg_1.2.5           codetools_0.2-18     future_1.31.0       
##  [10] withr_2.5.0          colorspace_2.0-3     fst_0.9.8           
##  [13] highr_0.10           knitr_1.41           rstudioapi_0.14     
##  [16] stats4_4.2.2         robustbase_0.99-0    ggsignif_0.6.4      
##  [19] listenv_0.9.0        labeling_0.4.2       emmeans_1.8.4-1     
##  [22] mnormt_2.1.1         bit64_4.0.5          farver_2.1.1        
##  [25] datawizard_0.9.0     rprojroot_2.0.3      coda_0.19-4         
##  [28] parallelly_1.34.0    vctrs_0.6.4          generics_0.1.3      
##  [31] TH.data_1.1-2        xfun_0.36            ggthemes_4.2.4      
##  [34] timechange_0.1.1     R6_2.5.1             VGAM_1.1-9          
##  [37] cachem_1.0.6         gridGraphics_0.5-1   assertthat_0.2.1    
##  [40] scales_1.2.1         vroom_1.6.0          multcomp_1.4-25     
##  [43] nnet_7.3-18          gtable_0.3.1         multcompView_0.1-9  
##  [46] globals_0.16.2       sandwich_3.0-2       rlang_1.1.2         
##  [49] MatrixModels_0.5-1   systemfonts_1.0.4    splines_4.2.2       
##  [52] rstatix_0.7.2        checkmate_2.1.0      yaml_2.3.6          
##  [55] abind_1.4-5          backports_1.4.1      Hmisc_5.1-1         
##  [58] tools_4.2.2          psych_2.3.3          lavaan_0.6-16       
##  [61] ggplotify_0.1.2      ellipsis_0.3.2       jquerylib_0.1.4     
##  [64] extraoperators_0.1.1 Rcpp_1.0.9           base64enc_0.1-3     
##  [67] ggpubr_0.6.0         rpart_4.1.19         zoo_1.8-11          
##  [70] cluster_2.1.4        fs_1.5.2             furrr_0.3.1         
##  [73] magrittr_2.0.3       data.table_1.14.8    magick_2.7.3        
##  [76] ggdist_3.3.0         SparseM_1.81         mvtnorm_1.1-3       
##  [79] mitml_0.4-5          hms_1.1.2            evaluate_0.19       
##  [82] xtable_1.8-4         gridExtra_2.3        shape_1.4.6         
##  [85] compiler_4.2.2       mice_3.16.0          crayon_1.5.2        
##  [88] minqa_1.2.5          htmltools_0.5.4      ggfun_0.1.3         
##  [91] mgcv_1.9-0           tzdb_0.3.0           Formula_1.2-4       
##  [94] MASS_7.3-58.1        boot_1.3-28          cli_3.6.1           
##  [97] quadprog_1.5-8       parallel_4.2.2       insight_0.19.7      
## [100] pan_1.9              pkgconfig_2.0.3      numDeriv_2016.8-1.1 
## [103] foreign_0.8-83       foreach_1.5.2        pbivnorm_0.6.0      
## [106] bslib_0.4.2          estimability_1.4.1   snakecase_0.11.0    
## [109] yulab.utils_0.1.0    distributional_0.3.2 digest_0.6.31       
## [112] parameters_0.21.3    rmarkdown_2.19       cellranger_1.1.0    
## [115] htmlTable_2.4.1      quantreg_5.94        jomo_2.7-6          
## [118] nloptr_2.0.3         lifecycle_1.0.3      nlme_3.1-160        
## [121] jsonlite_1.8.4       fansi_1.0.3          pillar_1.9.0        
## [124] lattice_0.21-9       fstcore_0.9.14       fastmap_1.1.0       
## [127] DEoptimR_1.1-2       survival_3.4-0       glue_1.6.2          
## [130] bayestestR_0.13.1    iterators_1.0.14     glmnet_4.1-8        
## [133] bit_4.0.5            stringi_1.7.8        sass_0.4.4          
## [136] textshaping_0.3.6    polspline_1.1.22     memoise_2.0.1